Normal Congruence Subgroups of Hecke Groups

Abstract

Hecke groups are an important class of discrete subgroups of PSL(2, ℝ), which play an important role in the study of Dirichlet series. Subgroups with finite index of a Hecke group, which are called congruence subgroups, are often used. Let q be a positive integer with [Formula: see text]. For the Hecke group [Formula: see text], the structures of principal congruence subgroups and normal congruence subgroups of level m are investigated in many papers, where m is a prime or a power of an odd prime. In this paper, we deal with the case that the level m is a power of 2.