Mathematical Research Letters

Volume 20 (2013)

Number 5

Level stripping for degree 2 Siegel modular forms

Pages: 919 – 932

DOI: http://dx.doi.org/10.4310/MRL.2013.v20.n5.a8

Author

Rodney Keaton (Department of Mathematical Sciences, Clemson University, Clemson, South Carolina, U.S.A.)

Abstract

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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