Explicit matrices for Hecke operators on Siegel modular forms

TL;DR

This paper provides explicit matrices representing the action of Hecke operators on Siegel modular forms, facilitating computational and theoretical analysis of these operators.

Contribution

It introduces explicit matrices for Hecke operators on Siegel modular forms, advancing computational methods in the field.

Findings

Explicit matrices for $T(p)$ and $T_j(p^2)$ Hecke operators

Enhanced tools for analyzing Siegel modular forms

Potential applications in computational number theory

Abstract

We present an explicit set of matrices giving the action of the Hecke operators $T(p)$, $T_j(p^2)$ on Siegel modular forms.