On Fourier coefficients of Siegel modular forms of degree two with respect to congruence subgroups

TL;DR

This paper derives a Petersson-type formula for Fourier coefficients of degree 2 Siegel cusp forms with respect to congruence subgroups and provides sharp upper bounds, extending previous work on the full modular case.

Contribution

It generalizes Kitaoka's method to congruence subgroups, enabling precise estimates of Fourier coefficients in this broader setting.

Findings

Established a Petersson-type formula for Fourier coefficients

Derived upper bounds for individual Fourier coefficients

Extended previous results from full modular forms to congruence subgroups

Abstract

We prove a formula of Petersson's type for Fourier coefficients of Siegel cusp forms of degree 2 with respect to congruence subgroups, and as a corollary, show upper bound estimates of individual Fourier coefficient. The method in this paper is essentially a generalization of Kitaoka's previous work which studied the full modular case, but some modification is necessary to obtain estimates which are sharp with respect to the level aspect.