Siegel and Hilbert Modular Forms
People: Nils Skoruppa, Nathan Ryan, Lassina Dembele
Status reports
Goal
Compute zeroes of the L-functions of the 27 icoshedral modular forms which were computed by Arnaud Jehanne (Bordeaux) - DONE!
Implement a class SiegelModularForms(SageObject) which provides an easy to use interfaceto all the basic functionalities of a Siegel modular forms of degree 2. Initialisation should in particular be possible using a pair (f,g) of elliptic modular forms ((f,g)\mapsto Jacobi form \mapsto Mass lift) or a file with precomputed Fourier coefficients. - ON THE WAY!
Compute the Fourier coefficients C([a,b,c]) of a basis of M_k(SP(2,Z)) for weights k\le 50 and
|b^2-4ac|\le 10000
Compute zeroes of the Spinor L-functions of the interesting (i.e. non-Maass cusp Hecke eigen) forms in these spaces
Compute Hilbert modular eigenforms for quadratic number fields Q(\sqrt D) for many D and weights, and compute zeroes of the associated L-functions
Strategy
- For Siegel modular forms we will merge Nathan's and Nils' existing programs.
- For Hilbert modularforms we use the new method of Lassina
Talks
Data
Weight 1 Icosahedral data at http://sage.math.washington.edu/home/nathan/weight-1-icosahedral-forms
Parallel weight 2 Hilbert Modular Forms over \mathbb{Q}(\sqrt{5}) of level of norm 31 data at http://sage.math.washington.edu/home/nathan/hilbert-forms/D5L31IDS10000 and http://sage.math.washington.edu/home/nathan/hilbert-forms/D5L31IDS20000/