Explicit spectral gap for Schottky subgroups of $\mathrm{S}\mathrm{L}(2,\mathbb{Z})$

Let $\mathrm{\Gamma }$ be a Schottky subgroup of $\mathrm{S}\mathrm{L}(2,\mathbb{Z})$. We establish a uniform and explicit lower bound of the second eigenvalue of the Laplace-Beltrami operator of congruence coverings of the hyperbolic surface $\mathrm{\Gamma }\mathrm{\backslash }{\mathbb{H}}^2$ provided the limit set of $\mathrm{\Gamma }$ is thick enough.