Hilbert modular forms of half-integral weight

The files below are the result of using the main result from
Nicolás Sirolli and Gonzalo Tornaría, Effective construction of Hilbert modular forms of half-integral weight,
for computing the central values twisted L-series attached to Hilbert modular forms. They extend the data available here, obtained using results from our previous articles.


Each of the files corresponds to a Hilbert modular form g, and is named after the label of g in the LMFDB database.

The files contain a header with commented information, including the quaternion algebra and the order R used in each case, along with the following lines: The main object of these computations are the lists cvs.

Each of these lists is made out of tuples (N,cvsN), which appear in the list sorted increasingly according to the absolute value of N.
Here cvsN is a list of tuples which have entries (D,λ(D),LD).
These entries include every integral D of type γ such that (D,O) is a fundamental discriminant having norm equal to N, and such that -lD belongs to a certain Shintani cone which serves as fundamental domain for the action of the group (Ox)2 acting on F+. Here the absolute value of N goes up to the precision Nmax indicated in the header.

Finally,
λ(D) = λ(D,O;f)
LD = L(1/2,g⊗χD)
are respectively the (D,O)-th Fourier coefficient of the theta series f corresponding to g and the central value of the L-series twisted by χD. They satisfy the central values formula
L(1/2,g⊗χD) = 2ω(D,N) · <g,g> · cg,γ / |D|1/2 · |λ(D,O;f)|2 / <f,f>.
See Theorem A from our article for notation and details.

Citations

Please reference this data as
Nicolás Sirolli and Gonzalo Tornaría, Hilbert modular forms of half-integral weight, Computational Number Theory, 2021. http://www.cmat.edu.uy/cnt/


[ICO]NameLast modifiedSizeDescription

[TXT]2.2.13.1-4.1-a.py2021-08-20 10:32 4.3KEven level
[TXT]3.3.49.1-27.1-a.py2021-08-20 10:32 7.8KCubic field
[TXT]2.2.40.1-89.1-a.py2021-08-20 10:32 13Kh(F) = 2
[TXT]2.2.5.1-55.1-a.py2021-08-20 10:32 30KComposite level
[TXT]14.2.a.a.py2021-08-20 10:32 44KEven level
[TXT]2.2.5.1-81.1-a.py2021-08-20 10:32 47KSquare level
[TXT]2.2.5.1-199.2-c.py2021-08-20 10:32 59KPrime level, L(g,1/2) = 0
[TXT]2.2.5.1-31.1-a.py2021-08-20 10:32 59KPrime level
[TXT]99.2.a.a.py2021-08-20 10:32 67KNon-square-free level, L(g,1/2) = 0
[TXT]50.2.a.a.py2022-05-20 17:45 73KEven, non-square-free level
[TXT]2.2.12.1-47.2-b.py2021-08-20 10:32 74Kh(F) = 1, h+(F) = 2
[TXT]75.2.a.b.py2021-08-20 10:32 75KNon-square-free level
[TXT]37.2.a.a.py2021-08-20 10:32 79KPrime level, L(g,1/2) = 0
[TXT]2.2.24.1-1.1-a.py2021-08-20 10:32 82KTrivial level
[TXT]15.2.a.a.py2021-08-20 10:32 88KComposite level
[TXT]57.2.a.a.py2021-08-20 10:32 89KComposite level, L(g,1/2) = 0
[TXT]58.2.a.a.py2021-08-20 10:32 89KEven level, L(g,1/2) = 0
[TXT]11.2.a.a.py2021-08-20 10:32 89KPrime level