The Maass Space for Paramodular Groups

TL;DR

This paper characterizes the Maass space for paramodular groups of degree 2 with squarefree level, demonstrating its invariance under Hecke operators and linking it to Siegel-Eisenstein series.

Contribution

It provides a new characterization of the Maass space for paramodular groups and proves its invariance under all Hecke operators, connecting it to Eisenstein series.

Findings

Maass space characterized for paramodular groups

Invariance under all Hecke operators established

Siegel-Eisenstein series shown to belong to Maass space

Abstract

In this paper we describe a characterization for the Maass space associated with the paramodular group of degree $2$ and squarefree level $N$. As an application we show that the Maass space is invariant under all Hecke operators. As a consequence we conclude that the associated Siegel-Eisenstein series belongs to the Maass space.