Computations of Vector-Valued Siegel Modular Forms
Journal of Number Theory
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.
Ghitza, Alexandru; Ryan, Nathan C.; and Sulon, David. "Computations of Vector-Valued Siegel Modular Forms." Journal of Number Theory 133, no. 11 (2013) : 3921-3940.