Let $\Gamma \subset \mathrm{SL}_2(\mathbf{Z})$ be a finite index subgroup. Let $X_\Gamma \to X(1)$ be the corresponding morphism of compact connected Riemann surfaces (obtained by adding the cusps).
Example. Take $\Gamma = \Gamma(n)$. Then $X_\Gamma = X(n)$.
What are the branch points of $X_\Gamma \to X(1)$.
Are they just the three points given by the elliptic points $0$ and $1728$ and the cusp $\infty$?