Congruence subgroups associated to the monster

Abstract

Let Δ = {G : g(G) = 0,Γ0(m) ≤ G ≤ N(Γ0(m)) for some m}, where N(Γ0(m)) is the normaliser of Γ0(m) in PSL2(ℝ) and g(G) is the genus of ℍ*/G. In this article, we determine all the m. Further, for each m, we list all the intermediate groups G of Γ0(m) ≤ N(Γ0(m)) such that g(G) - 0. All the intermediate groups of width 1 at ∞ are also listed in a separate table (see www.math.nus.edu.sg/ ~matlml/).