Layout of the Siegel modular forms part
- Entry page listing rings/modules of Siegel modular forms where generators are explicitly known
- For each known ring/module a page containing:
- If it is module of vector valued forms a link to the base ring of Siegel modular forms
- an interactive part to compute dimensions of graded parts of this ring.
- A link to Siegel modular forms of this ring/module which are available in the database.
- These Siegel modular forms include the generators and a good choice of Hecke eigenforms.
- The relations satisfied by the generators
- For each of the Siegel modular form mentioned above a page containing:
- closed formulas (if available): Borcherds product, Maass lift, product of theta characteristics etc.
- expression as polynomial in the generators
- Links to the database containing:
- the Fourier coefficients
- eigenvalues (if it is a Hecke eigenform)
- Links to its associated L-functions in the L-function pages (if it is a Hecke eigenform)
- Links to its Fourier Jacobi coefficients in the Jacobi forms pages
- Friends: Jacobi forms (if it is a Maass lift), Elliptic modular forms (if it is a Maass lift or Yoshida lift, if it satisfies congruences),
- miscellaneous informations (e.g. L-function is the L-function of a variety etc.)
- Further data can be computed with the Siegel modular forms package which was submitted to Sage.
Remarks
Data exist already on http://data.countnumber.de/Siegel-Modular-Forms/.
Available rings/modules of Siegel modular forms
- Sp(2,Z) integral weight
\Gamma_0(2), \Gamma_0^{\psi_3}(3), \Gamma_0^{\psi_4}(4) Ibukiyama 1
\Gamma_0(3) Ibukiyama 2
M_{*,2}({\rm Sp}(2,Z)) Satoh