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

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