/************************************************************/ /* Authors : Gustavo Rama, Gonzalo Tornaria * Date : June 2020 * * Table of orthogonal modular forms of square-free level up to 1000 * * Excluding Gritsenko and Yoshida lifts. * * Please reference this data as * * Gustavo Rama and Gonzalo Tornaría, * Quinary orthogonal modular forms, 2020. * http://www.cmat.edu.uy/cnt/ * * and its companion paper * * Gustavo Rama and Gonzalo Tornaría, * Computation of paramodular forms, * ANTS 2020. * * The format for each entry is * * [level, class, dimension, root_numbers, ap_values, ap2_values] * * */ {forms_squarefree=[ [61, "a", 1, [[61, -1]], [[2, -7], [3, -3], [5, 3], [7, -9], [11, -4], [13, -3]], [[2, 7], [3, -9], [5, -9]]], [69, "a", 1, [[3, -1], [23, 1]], [[2, -6], [3, -4], [5, 8], [7, -12], [11, 2], [13, -35]], [[2, 5], [5, -32]]], [73, "a", 1, [[73, -1]], [[2, -6], [3, -2], [5, 0], [7, 7], [11, -66], [13, 16]], [[2, 6], [3, -9], [5, 0]]], [79, "a", 1, [[79, -1]], [[2, -5], [3, -5], [5, 3], [7, 15], [11, 26], [13, -15]], [[2, 2], [3, 4], [5, -10]]], [82, "a", 1, [[2, 1], [41, -1]], [[2, -5], [3, -4], [5, -2], [7, 10], [11, -40], [13, 28]], [[3, -2], [5, -60]]], [85, "a", 1, [[5, -1], [17, 1]], [[2, -4], [3, -8], [5, 9], [7, 8], [11, -10], [13, 34]], [[2, -1], [3, 6]]], [87, "a", 1, [[3, -1], [29, 1]], [[2, -5], [3, -2], [5, -1], [7, 10], [11, -3], [13, -19]], [[2, 4], [5, -26]]], [89, "a", 1, [[89, -1]], [[2, -4], [3, -6], [5, 16], [7, -17], [11, -2], [13, -46]], [[2, 2], [3, -6], [5, 27]]], [91, "a", 1, [[7, -1], [13, 1]], [[2, -5], [3, -1], [5, -5], [7, 12], [11, -18], [13, -1]], [[2, 4], [3, -10], [5, -16]]], [93, "a", 1, [[3, 1], [31, -1]], [[2, -4], [3, -5], [5, 3], [7, 17], [11, -10], [13, 0]], [[2, 1], [5, -26]]], [94, "a", 1, [[2, 1], [47, -1]], [[2, -5], [3, -1], [5, -13], [7, 8], [11, -12], [13, -59]], [[3, -17], [5, 9]]], [94, "b", 1, [[2, -1], [47, 1]], [[2, -3], [3, -11], [5, 3], [7, -4], [11, -8], [13, 25]], [[3, 15], [5, -39]]], [97, "a", 2, [[97, -1]], [[2, -9], [3, -4], [5, -4], [7, 16], [11, -64], [13, 24]], [[2, 6], [3, -14], [5, 4]]], [101, "a", 2, [[101, -1]], [[2, -7], [3, -11], [5, 22], [7, -32], [11, 46], [13, -54]], [[2, 2], [3, 0], [5, -21]]], [103, "a", 2, [[103, -1]], [[2, -9], [3, -2], [5, -15], [7, 26], [11, -9], [13, 29]], [[2, 5], [3, -10], [5, -30]]], [105, "a", 1, [[3, -1], [5, 1], [7, 1]], [[2, -3], [3, -7], [5, 3], [7, 5], [11, -32], [13, -10]], [[2, -2]]], [106, "a", 1, [[2, -1], [53, 1]], [[2, -3], [3, -8], [5, -12], [7, 16], [11, 36], [13, -61]], [[3, 5], [5, 3]]], [106, "b", 1, [[2, 1], [53, -1]], [[2, -3], [3, -6], [5, 6], [7, 10], [11, -48], [13, 11]], [[3, -1], [5, -15]]], [109, "a", 3, [[109, -1]], [[2, -10], [3, -15], [5, -7], [7, 37], [11, 27], [13, 20]], [[2, -3], [3, 7], [5, -20]]], [111, "a", 2, [[3, 1], [37, -1]], [[2, -8], [3, -4], [5, -12], [7, 14], [11, 62], [13, -36]], [[2, 2], [5, -48]]], [113, "a", 1, [[113, -1]], [[2, -3], [3, -4], [5, 8], [7, 4], [11, -4], [13, -40]], [[2, 2], [3, -4], [5, -4]]], [114, "a", 1, [[2, 1], [3, -1], [19, 1]], [[2, -4], [3, -1], [5, -9], [7, 9], [11, 19], [13, 4]], [[5, -18]]], [115, "a", 1, [[5, -1], [23, 1]], [[2, -4], [3, -1], [5, -7], [7, 2], [11, 12], [13, 21]], [[2, 1], [3, -16]]], [118, "a", 1, [[2, -1], [59, 1]], [[2, -2], [3, -9], [5, -3], [7, 9], [11, -66], [13, 34]], [[3, 4], [5, -14]]], [118, "b", 2, [[2, 1], [59, -1]], [[2, -8], [3, -2], [5, -18], [7, 18], [11, 24], [13, 20]], [[3, -4], [5, -12]]], [119, "a", 1, [[7, -1], [17, 1]], [[2, -3], [3, -4], [5, 4], [7, -9], [11, 82], [13, -66]], [[2, 0], [3, -8], [5, -36]]], [123, "a", 1, [[3, -1], [41, 1]], [[2, -3], [3, -3], [5, -4], [7, 16], [11, -2], [13, 10]], [[2, 0], [5, 12]]], [127, "a", 3, [[127, -1]], [[2, -9], [3, -9], [5, -12], [7, 45], [11, 18], [13, 69]], [[2, 0], [3, 6], [5, -12]]], [129, "a", 1, [[3, -1], [43, 1]], [[2, -2], [3, -6], [5, 14], [7, -22], [11, 21], [13, -6]], [[2, 0], [5, -9]]], [129, "b", 3, [[3, 1], [43, -1]], [[2, -10], [3, -8], [5, -14], [7, 4], [11, -31], [13, -6]], [[2, 0], [5, -37]]], [130, "a", 1, [[2, 1], [5, -1], [13, 1]], [[2, -3], [3, -2], [5, -7], [7, 16], [11, -22], [13, 43]], [[3, -6]]], [130, "b", 1, [[2, 1], [5, 1], [13, -1]], [[2, -1], [3, -10], [5, 15], [7, 4], [11, -2], [13, -15]], [[3, 10]]], [131, "a", 2, [[131, -1]], [[2, -6], [3, -4], [5, 8], [7, -10], [11, 64], [13, -84]], [[2, 4], [3, -8], [5, -4]]], [133, "a", 1, [[7, 1], [19, -1]], [[2, -3], [3, -2], [5, -11], [7, 26], [11, 31], [13, 6]], [[2, -1], [3, -2], [5, 8]]], [133, "b", 1, [[7, -1], [19, 1]], [[2, -3], [3, -1], [5, 0], [7, -2], [11, -54], [13, 29]], [[2, 2], [3, -18], [5, 0]]], [133, "c", 2, [[7, -1], [19, 1]], [[2, -8], [3, -2], [5, -12], [7, 0], [11, 16], [13, 114]], [[2, 2], [3, 10], [5, -48]]], [134, "a", 1, [[2, 1], [67, -1]], [[2, -3], [3, -2], [5, -1], [7, -9], [11, 83], [13, -65]], [[3, -6], [5, -15]]], [134, "b", 1, [[2, -1], [67, 1]], [[2, -1], [3, -10], [5, 7], [7, -7], [11, -15], [13, -5]], [[3, 10], [5, 21]]], [137, "a", 2, [[137, -1]], [[2, -4], [3, -10], [5, 12], [7, 0], [11, 16], [13, -8]], [[2, 0], [3, 8], [5, 12]]], [138, "a", 1, [[2, -1], [3, 1], [23, 1]], [[2, -2], [3, -6], [5, -12], [7, 12], [11, 14], [13, -7]], [[5, 12]]], [139, "a", 4, [[139, -1]], [[2, -14], [3, -4], [5, -22], [7, 14], [11, -6], [13, 76]], [[2, 4], [3, -10], [5, -26]]], [141, "a", 1, [[3, -1], [47, 1]], [[2, -5], [3, 4], [5, -9], [7, -7], [11, 37], [13, 43]], [[2, 3], [5, 21]]], [141, "b", 1, [[3, 1], [47, -1]], [[2, -1], [3, -8], [5, 13], [7, -3], [11, 21], [13, -21]], [[2, -1], [5, 7]]], [141, "c", 2, [[3, -1], [47, 1]], [[2, -4], [3, -9], [5, -10], [7, 29], [11, 4], [13, -20]], [[2, -4], [5, -56]]], [142, "a", 2, [[2, 1], [71, -1]], [[2, -5], [3, -5], [5, -14], [7, 37], [11, -28], [13, -7]], [[3, -10], [5, -6]]], [142, "b", 2, [[2, -1], [71, 1]], [[2, -3], [3, -15], [5, -8], [7, 9], [11, -22], [13, 69]], [[3, 14], [5, 2]]], [143, "a", 1, [[11, 1], [13, -1]], [[2, -2], [3, -3], [5, 1], [7, 12], [11, 11], [13, -69]], [[2, 1], [3, -8], [5, -18]]], [145, "a", 2, [[5, -1], [29, 1]], [[2, -6], [3, -2], [5, -16], [7, 24], [11, -62], [13, 114]], [[2, 0], [3, -12]]], [145, "b", 3, [[5, 1], [29, -1]], [[2, -5], [3, -19], [5, 6], [7, -20], [11, -17], [13, 57]], [[2, -8], [3, -8]]], [146, "a", 2, [[2, 1], [73, -1]], [[2, -5], [3, -7], [5, 9], [7, -34], [11, 79], [13, -7]], [[3, -4], [5, -50]]], [149, "a", 4, [[149, -1]], [[2, -6], [3, -23], [5, 16], [7, -17], [11, 77], [13, -9]], [[2, -6], [3, 12], [5, -15]]], [151, "a", 5, [[151, -1]], [[2, -12], [3, -17], [5, -33], [7, 57], [11, 81], [13, 75]], [[2, -9], [3, 12], [5, -28]]], [154, "a", 1, [[2, 1], [7, 1], [11, -1]], [[2, -2], [3, -3], [5, -1], [7, -5], [11, -1], [13, -2]], [[3, -16], [5, -54]]], [154, "b", 2, [[2, -1], [7, 1], [11, 1]], [[2, -4], [3, -10], [5, -26], [7, 14], [11, 18], [13, -52]], [[3, -8], [5, -20]]], [155, "a", 1, [[5, -1], [31, 1]], [[2, -2], [3, -2], [5, 2], [7, 3], [11, 26], [13, 20]], [[2, 1], [3, -4]]], [157, "a", 2, [[157, -1]], [[2, -6], [3, 2], [5, -14], [7, 8], [11, -36], [13, 46]], [[2, 2], [3, -22], [5, -12]]], [157, "b", 5, [[157, -1]], [[2, -15], [3, -12], [5, 0], [7, -11], [11, 9], [13, 217]], [[2, 3], [3, 16], [5, -78]]], [158, "a", 1, [[2, -1], [79, 1]], [[2, -1], [3, -7], [5, -1], [7, -7], [11, 22], [13, 13]], [[3, 4], [5, -18]]], [159, "a", 1, [[3, -1], [53, 1]], [[2, -3], [3, 2], [5, -10], [7, 20], [11, -20], [13, 39]], [[2, 2], [5, -8]]], [159, "b", 1, [[3, 1], [53, -1]], [[2, -2], [3, -2], [5, 6], [7, -10], [11, 72], [13, -19]], [[2, 1], [5, -10]]], [159, "c", 3, [[3, -1], [53, 1]], [[2, -11], [3, -2], [5, -12], [7, -16], [11, 50], [13, 11]], [[2, 2], [5, -54]]], [161, "a", 1, [[7, -1], [23, 1]], [[2, -1], [3, -6], [5, 4], [7, -1], [11, 34], [13, 18]], [[2, -2], [3, 0], [5, -4]]], [161, "b", 3, [[7, 1], [23, -1]], [[2, -4], [3, -17], [5, 4], [7, -33], [11, 50], [13, -127]], [[2, -7], [3, -12], [5, -56]]], [163, "a", 4, [[163, -1]], [[2, -10], [3, -4], [5, -16], [7, 38], [11, 4], [13, 84]], [[2, 2], [3, -8], [5, -12]]], [165, "a", 1, [[3, -1], [5, 1], [11, 1]], [[2, -1], [3, -4], [5, 6], [7, 4], [11, 7], [13, -28]], [[2, 1]]], [165, "b", 2, [[3, 1], [5, -1], [11, 1]], [[2, -5], [3, -7], [5, -17], [7, -4], [11, 68], [13, 2]], [[2, -8]]], [166, "a", 1, [[2, 1], [83, -1]], [[2, -4], [3, 3], [5, -8], [7, -3], [11, -9], [13, 92]], [[3, 4], [5, -12]]], [166, "b", 3, [[2, 1], [83, -1]], [[2, -10], [3, -3], [5, -14], [7, 2], [11, 51], [13, -112]], [[3, -21], [5, -54]]], [166, "c", 3, [[2, -1], [83, 1]], [[2, -4], [3, -17], [5, -18], [7, -14], [11, -9], [13, 54]], [[3, -5], [5, 16]]], [167, "a", 1, [[167, 1]], [[2, -8], [3, -10], [5, -4], [7, -14], [11, -22], [13, -4]], [[2, 10], [3, 11], [5, -44]]], [167, "b", 1, [[167, -1]], [[2, -2], [3, 0], [5, -2], [7, 2], [11, -14], [13, -34]], [[2, 2], [3, -17], [5, 16]]], [167, "c", 2, [[167, -1]], [[2, -3], [3, -9], [5, 2], [7, 3], [11, 92], [13, -41]], [[2, -3], [3, 12], [5, -28]]], [170, "a", 1, [[2, 1], [5, 1], [17, -1]], [[2, -2], [3, -2], [5, 1], [7, -14], [11, 24], [13, 4]], [[3, -12]]], [173, "a", 1, [[173, 1]], [[2, -8], [3, -9], [5, -10], [7, -4], [11, -4], [13, -72]], [[2, 10], [3, 7], [5, -3]]], [173, "b", 1, [[173, -1]], [[2, -2], [3, -1], [5, 0], [7, -16], [11, -24], [13, 2]], [[2, 0], [3, -23], [5, -9]]], [173, "c", 4, [[173, -1]], [[2, -7], [3, -15], [5, 14], [7, -27], [11, 92], [13, 43]], [[2, -2], [3, 22], [5, -90]]], [174, "a", 1, [[2, -1], [3, 1], [29, 1]], [[2, -3], [3, -2], [5, -13], [7, -14], [11, 47], [13, 21]], [[5, -14]]], [174, "b", 1, [[2, 1], [3, 1], [29, -1]], [[2, -3], [3, 2], [5, -13], [7, 12], [11, -17], [13, 3]], [[5, 4]]], [174, "c", 1, [[2, -1], [3, -1], [29, -1]], [[2, -1], [3, -6], [5, 3], [7, -36], [11, 29], [13, -13]], [[5, -12]]], [174, "d", 1, [[2, -1], [3, 1], [29, 1]], [[2, 0], [3, -8], [5, -1], [7, 10], [11, -43], [13, 45]], [[5, -26]]], [177, "a", 2, [[3, 1], [59, -1]], [[2, -2], [3, -8], [5, 10], [7, -14], [11, 36], [13, -24]], [[2, 0], [5, -4]]], [177, "b", 4, [[3, -1], [59, 1]], [[2, -9], [3, -6], [5, -16], [7, 30], [11, -32], [13, 34]], [[2, -1], [5, 4]]], [178, "a", 2, [[2, -1], [89, 1]], [[2, -3], [3, -8], [5, -24], [7, 11], [11, -6], [13, 49]], [[3, -3], [5, 24]]], [178, "b", 5, [[2, 1], [89, -1]], [[2, -12], [3, -11], [5, -17], [7, 23], [11, -58], [13, 143]], [[3, 5], [5, -102]]], [179, "a", 4, [[179, -1]], [[2, -6], [3, -10], [5, -6], [7, 2], [11, 134], [13, -134]], [[2, -2], [3, -8], [5, -32]]], [181, "a", 10, [[181, -1]], [[2, -27], [3, -16], [5, -14], [7, -38], [11, 59], [13, 249]], [[2, 0], [3, -24], [5, -91]]], [182, "a", 1, [[2, -1], [7, -1], [13, -1]], [[2, -1], [3, -5], [5, -3], [7, -18], [11, 6], [13, 33]], [[3, -6], [5, -12]]], [183, "a", 1, [[3, 1], [61, -1]], [[2, -2], [3, -3], [5, -9], [7, 3], [11, 49], [13, 51]], [[2, -5], [5, -18]]], [183, "b", 1, [[3, -1], [61, 1]], [[2, -1], [3, -3], [5, 3], [7, -3], [11, 43], [13, -33]], [[2, 0], [5, 6]]], [183, "c", 3, [[3, 1], [61, -1]], [[2, -3], [3, -11], [5, -19], [7, 49], [11, -43], [13, 33]], [[2, -4], [5, -30]]], [185, "a", 2, [[5, 1], [37, -1]], [[2, -1], [3, -11], [5, 17], [7, -5], [11, -45], [13, 69]], [[2, 0], [3, 2]]], [185, "b", 4, [[5, -1], [37, 1]], [[2, -9], [3, -7], [5, 9], [7, -55], [11, 79], [13, -53]], [[2, 0], [3, -26]]], [186, "a", 1, [[2, -1], [3, 1], [31, 1]], [[2, 0], [3, -7], [5, -1], [7, -3], [11, 74], [13, -102]], [[5, -34]]], [186, "b", 2, [[2, -1], [3, -1], [31, -1]], [[2, -4], [3, -6], [5, -26], [7, -2], [11, 16], [13, -16]], [[5, 36]]], [186, "c", 2, [[2, 1], [3, -1], [31, 1]], [[2, -4], [3, -2], [5, -10], [7, 6], [11, -24], [13, 68]], [[5, -12]]], [187, "a", 2, [[11, 1], [17, -1]], [[2, -6], [3, 2], [5, -10], [7, 0], [11, -10], [13, 28]], [[2, 0], [3, -12], [5, -60]]], [187, "b", 2, [[11, -1], [17, 1]], [[2, -4], [3, 0], [5, -18], [7, 10], [11, -8], [13, 16]], [[2, -2], [3, -26], [5, -16]]], [190, "a", 1, [[2, 1], [5, 1], [19, -1]], [[2, -2], [3, 1], [5, -17], [7, 19], [11, -30], [13, -17]], [[3, -18]]], [190, "b", 1, [[2, -1], [5, 1], [19, 1]], [[2, 0], [3, 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