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

Let \Gamma be a Schottky subgroup of \mathrm{SL}(2,\mathbb{Z}) and let X be the corresponding hyperbolic surface. Provided that the limit set of \Gamma is thick enough, we give an explicit interval I_{\Gamma} = [0,a_{\Gamma}] such that for most congruence coverings X_{n} of X , the eigenvalues in I_{\Gamma} of the Laplace–Beltrami operators of X_{n} and X , as well as their multiplicities, coincide.