A sparse equidistribution result for $(\mathrm{S}\mathrm{L}(2,\mathbb{R})\mathrm{/}{\mathrm{\Gamma }}_0{)}^n$

Let $G=\mathrm{S}\mathrm{L}(2,\mathbb{R}{)}^n$, let $\mathrm{\Gamma }={\mathrm{\Gamma }}_0^n$, where ${\mathrm{\Gamma }}_0$ is a co-compact lattice in $\mathrm{S}\mathrm{L}(2,\mathbb{R})$, let $F(\mathbf{x})$ be a non-singular quadratic form and let $u(x_1,\mathrm{.}\mathrm{.}\mathrm{.},x_n)$ denote the unipotent elements in $G$ which generate the standard $n$ dimensional horospherical subgroup, consisting of $2\times 2$ upper triangular unipotent matrices in each co-ordinate. We prove that in absence of any local obstructions for $F$, given any $x_0\in G\mathrm{/}\mathrm{\Gamma }$, the sparse subset $\{u(\mathbf{x})x_0:\in {\mathbb{Z}}^n,F(\mathbf{x})=0\}$ equidistributes in $G\mathrm{/}\mathrm{\Gamma }$ as long as $n\ge 481$, independent of the spectral gap of ${\mathrm{\Gamma }}_0$.