Level stripping for degree 2 Siegel modular forms

In this paper, we consider stripping primes from the level of degree 2 cuspidal Siegel eigenforms. Specifically, given an eigenform of level ${N\ell}^r $under certain restrictions, where $\ell \nmid N$ is a prime, we construct an eigenform of level $N$, which is congruent in eigenvalues to our original form. To obtain our results, we use constructions of Eisenstein series and theta functions to adapt ideas from a level stripping result on elliptic modular forms.

Keywords

congruence of modular forms, Galois representations, Siegel modular forms

2010 Mathematics Subject Classification

Primary 11F33, 11F46. Secondary 11F80.

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Published 28 April 2014