 Cusp of a modular group

A cusp of a finite-index subgroup $\Gamma \le S{L}_2(\mathbb{Z})$ is an orbit in $\Gamma \backslash {\mathbb{P}}^1(\mathbb{Q})$. If $\sigma \in S{L}_2(\mathbb{Z})$ sends infinity to a cusp, behavior there is studied through $f{|}_k\sigma$.