Maass Spezialschar of level N

Abstract

In this paper the image of the Saito-Kurokawa lift of level $N$ with Dirichlet character is studied. We give a new characterization of this so called Maass Spezialschar of level $N$ by symmetries involving Hecke operators related to $\Gamma_0(N)$. We finally obtain for all prime numbers $p$ local Maass relations. This generalizes known results for level $N=1$