Automorphy factor
= Automorphy factor
{title2=$j(\gamma,\tau)=c\tau+d$}
For $\gamma=\begin{pmatrix}a&b\\c&d\end{pmatrix}$, the automorphy factor is $j(\gamma,\tau)=c\tau+d$. It obeys the cocycle identity
$$
j(\gamma\delta,\tau)=j(\gamma,\delta\tau)j(\delta,\tau).
$$