Date of Award
Doctor of Philosophy (PhD)
Associate Professor Jim Brown
Professor Kevin James
Associate Professor Hui Xue
Assistant Professor Michael Burr
In this Dissertation we consider stripping primes from the level of genus 2 cuspidal Siegel eigenforms. Specifically, given an eigenform of level Nlr which satisfies certain mild conditions, where l is a prime not dividing N, we construct an eigenform of level N which is congruent to our original form. To obtain our results, we use explicit constructions of Eisenstein series and theta functions to adapt ideas from a level stripping result on elliptic modular forms. Furthermore, we give applications of this result to Galois representations and provide evidence for an analog of Serre's conjecture in the genus 2 case.
Keaton, Rodney, "Level stripping of genus 2 Siegel modular forms" (2014). All Dissertations. 1294.