}$$ $$= \mathrm{vol}({\Gamma\backslash G})f(0) + \frac{\mathrm{vol}(Q_{{\mathbb{Z}}} \backslash K )}{\mathrm{vol}(\mathrm{SO}_{n-0})}\sum_{\ell >0} \int_{Q_{{\mathbb{Z}}} \backslash ( N'M)}\int_{A'} {f(\ell en'ma')\displaystyle t^n da'