On the Cusp Forms of Congruence Subgroups of an almost Simple Lie group

Abstract

In this paper we address the issue of existence of cusp forms for almost simple Lie groups using the approach of the second author combined with local information on supercuspidal representations for $p$-adic groups known by the first author. We pay special attention to the case of $SL_M(\Bbb R)$ where we prove various existence results for principal congruence subgroups.