Computations of Vector-Valued Siegel Modular Forms

Authors

Alexandru Ghitza
Nathan C. Ryan, Bucknell UniversityFollow
David SulonFollow

Publication Date

2013

Description

We carry out some computations of vector-valued Siegel modular forms of degree two, weight (k, 2) and level one, and highlight three experimental results: (1) we identify a rational eigenform in a three-dimensional space of cusp forms; (2) we observe that non-cuspidal eigenforms of level one are not always rational; (3) we verify a number of cases of conjectures about congruences between classical modular forms and Siegel modular forms. Our approach is based on Satoh's description of the module of vector-valued Siegel modular forms of weight (k, 2) and an explicit description of the Hecke action on Fourier expansions. (C) 2013 Elsevier Inc. All rights reserved.

Journal

Journal of Number Theory

Volume

133

Issue

11

First Page

3921

Last Page

3940

Department

Mathematics

Link to Published Version

dx.doi.org/10.1016/j.jnt.2013.04.024

Recommended Citation

Ghitza, Alexandru; Ryan, Nathan C.; and Sulon, David. "Computations of Vector-Valued Siegel Modular Forms." Journal of Number Theory (2013) : 3921-3940.