A First Course in Modular Forms
《A First Course in Modular Forms》 · 第 14 页 · Section 1.1「First definitions and examples」
For any matrix $\gamma=\left(\begin{smallmatrix}a&b\\c&d\end{smallmatrix}\right)\in\mathrm{SL}_2(\mathbb Z)$ define the factor of automorphy $j(\gamma,\tau)\in\mathbb C$ for $\tau\in\mathbb H$ to be $j(\gamma,\tau)=c\tau+d$.