Operators on the Space of Modular Forms

Abstract

Let G be a group, Г, Г′ be subgroups of G. Then Г and Г′ are commensurable if Г ∩ Г′ is of finite index in Г and in Г′. We write Г ∼ Г′ if Г and Г′ are commensurable. For any subgroup Г of G, put

$$ \widetilde\Gamma - \left\{ {\left. {\alpha \in G} \right|\alpha \Gamma \alpha ^{ - 1} \sim \Gamma } \right\}. $$

.