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Computations of vector-valued Siegel modular forms

Authors
Journal
Journal of Number Theory
0022-314X
Publisher
Elsevier
Volume
133
Issue
11
Identifiers
DOI: 10.1016/j.jnt.2013.04.024
Keywords
  • Siegel Modular Forms
  • Critical Values
  • Congruences Between Modular Forms

Abstract

Abstract 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 Satohʼs 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.

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