The normalizer of Γ0(N) in PSL(2, ℝ)

Let Γ denote the modular group, consisting of the Mobius transformations As usual we denote the above transformation by the matrix remembering that V and – V represent the same transformation. If N is a positive integer we let Γ 0 ( N ) denote the transformations for which c ≡ 0 mod N . Then Γ 0 ( N ) is a subgroup of index the product being taken over all prime divisors of N .