Genus 2 paramodular Eisenstein congruences

TL;DR

This paper explores Eisenstein congruences for genus 2 paramodular forms at level p, providing computational evidence and algorithms to generate Hecke eigenvalues, supporting Harder's conjecture.

Contribution

It introduces explicit algorithms for computing Hecke eigenvalues of genus 2 paramodular forms, offering new evidence for Eisenstein congruences and Harder's conjecture.

Findings

Confirmed Eisenstein congruences numerically for specific levels

Developed algorithms for computing Hecke eigenvalues

Provided computational support for theoretical conjectures

Abstract

We investigate certain Eisenstein congruences, as predicted by Harder, for level p paramodular forms of genus 2. We use algebraic modular forms to generate new evidence for the conjecture. In doing this we see explicit computational algorithms that generate Hecke eigenvalues for such forms.