$\PSL_2$-index (awaiting review)

The $\PSL_2$-index of a modular curve $X_H$ is the index of $\Gamma_H := \pm H\cap \SL_2(\Z)$ in $\PSL_2(\Z)$; this index is also the degree of the map $j : \Gamma_H \backslash \overline{\mathfrak{h}} \to X(1)$, where $\overline{\mathfrak{h}}$ is the completed upper half-plane. This is equal to the index of the modular curve when $-1 \in H$, and equals half the index if $-1 \notin H$.