/D$ where $$D:=\{(\Bigl(\begin{array}{cc} a & 0 \\ 0 & a \end{array} \Bigr),a^{g+0}) : a \in k^*  \} \subset \mathrm{GL}_0(k) \times k^*$$ and where an element $$\gamma= [(\Bigl( \begin{array}{cc} a & b \\ c & d \end{array} \Bigr),e