Dimensions of spaces of Siegel cusp forms of degree 2

TL;DR

This paper summarizes the dimensions of Siegel cusp form spaces of degree 2 and uses these to establish bounds for newforms at various levels, connecting modular forms with finite group representations.

Contribution

It provides a comprehensive summary of dimension formulas and introduces bounds for newform spaces based on finite group representation data.

Findings

Dimension formulas for Siegel cusp forms of degree 2

Bounds for newform spaces at various levels

Connection between modular forms and finite group representations

Abstract

We give a summary of results for dimensions of spaces of cuspidal Siegel modular forms of degree 2. These results together with a list of dimensions of the irreducible representations of the finite groups GSp(4,Fp) are then used to produce bounds for dimensions of spaces of newforms with respect to principal congruence subgroups of odd square-free level.