The group structure of the normalizer of ${\Gamma }_0(N)$

Abstract

We determine the group structure of the normalizer of ${\Gamma }_0(N)$ in $S{L}_2(\mathbb{R})$ modulo ${\Gamma }_0(N)$. These results correct the Atkin-Lehner statement at the paper Hecke operators of ${\Gamma }_0(N)$.