 $$\mathrm{vol}({\Gamma\backslash G})f(0) + \frac{\mathrm{vol}({\mathbb{S}}^{n-0}) }{\# (\mathrm{SO}_{n-0}({\mathbb{Z}}))} \mathrm{vol}(\mathrm{SL}_{n-0}( {\mathbb{Z}}) \backslash \mathrm{SL}_{n-0}( {\mathbb{R}})) \sum_{\ell >0} \int_{