On computing finite index subgroups of PSL2(ℤ)

Abstract

We present a method to compute finite index subgroups of PSL2(ℤ). Our strategy follows Kulkarni’s ideas, the main contribution being a recursive method to compute bivalent trees as well as their automorphism groups. As a concrete application, we compute all subgroups of index up to [Formula: see text]. We then use this database to produce tables with several arithmetical properties.