On distinguishing Siegel cusp forms of degree two

TL;DR

This paper presents methods to distinguish Siegel cusp forms of degree two, showing that certain eigenforms can be uniquely identified by their eigenvalues and $L$-functions.

Contribution

The work introduces new criteria for identifying Siegel cusp forms of degree two using Hecke eigenvalues and $L$-functions.

Findings

A Hecke eigenform of level one can be determined by its second eigenvalue under specific assumptions.

Two level one Hecke eigenforms can be distinguished using their $L$-functions.

Abstract

In this work, we establish several results on distinguishing Siegel cusp forms of degree two. In particular, a Hecke eigenform of level one can be determined by its second Hecke eigenvalue under a certain assumption. Moreover, we can distinguish two Hecke eigenforms of level one by using $L$-functions.