Index of a modular map (awaiting review)

Given a map $f : X_G \to X_H$ of modular curves induced by an inclusion of open subgroups $H \le G \le \GL_2(\hat{\Z})$, the relative index of $f$ is the index $[G : H]$. The degree of $f$ is half the index of $f$ if $-1 \in G$ and $-1 \not\in H$, and equal to the index otherwise.