Computations of vectorvalued Siegel modular forms
Abstract
We carry out some computations of vector valued Siegel modular forms of degree two, weight (k,2) and level one. Our approach is based on Satoh's description of the module of vectorvalued Siegel modular forms of weight (k, 2) and an explicit description of the Hecke action on Fourier expansions. We highlight three experimental results: (1) we identify a rational eigenform in a three dimensional space of cusp forms, (2) we observe that noncuspidal eigenforms of level one are not always rational and (3) we verify a number of cases of conjectures about congruences between classical modular forms and Siegel modular forms.
 Publication:

arXiv eprints
 Pub Date:
 March 2012
 arXiv:
 arXiv:1203.5611
 Bibcode:
 2012arXiv1203.5611G
 Keywords:

 Mathematics  Number Theory;
 11F33;
 11F46;
 11F60;
 11Y99
 EPrint:
 18 pages, 2 tables