  For $\Gamma$ a Fuchsian Group of the first kind, we obtain large sieve
inequalities with weights the hyperbolic periods of Maass forms of even weight.
This is inspired by work of Chamizo, who proved a large sieve inequality with
weights values of Maass forms of weight $0$. The motivation is applications in
counting problems in $\Gamma_1 \backslash \Gamma / \Gamma_2$, where $\Gamma_1$,
$\Gamma_2$ are hyperbolic subgroups of $\Gamma$.
