Index of a modular curve (awaiting review)

The index of a modular curve $X_H$ is the index of the open subgroup $H\leq \GL_2(\widehat\Z)$. The degree of the canonical morphism $j \colon X_H\to X(1)\simeq \mathbb P^1$ equals the index when $-1 \in H$, and equals half the index if $-1 \notin H$.