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{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
$$
j(\gamma\delta,\tau)=j(\gamma,\delta\tau)j(\delta,\tau).
$$


Automorphy factor

Determinant-normalized slash operator

Hecke-normalized rational slash operator

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Automorphy factor ( $j (γ, τ) = c τ + d$ )

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Automorphy factor (j(γ,τ)=cτ+d)

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Automorphy factor ( $j (γ, τ) = c τ + d$ )

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