On Eichler's trace formula
Hiroshi Saitō · Journal of the Mathematical Society of Japan · 1972
Let $G=GL(2, R)^{+}$ be the subgroup of $GL(2, R)$ consisting of the elements of $GL(2, R)$ such as $\det>0$ .Let $H$ be the complex upper half plane.We regard $G$ as a group of transformations on-1}$ is commen- surable with $\Gamma$ and denote by $\Gamma^{\prime}$ the subgroup of $G$ generated by $\Gamma$ and $\alpha$ .Let $\chi$ be a linear character of $\Gamma^{\prime}$ .We assume that $\chi(\epsilon)=1$ for $\epsilon\in Z(\Gamma)=$ $ Z(G)_{\Gamma 1}\Gamma$