= Determinant-normalized slash operator
{title2=$f|_k\gamma=(\det\gamma)^{k/2}(cz+d)^{-k}f(\gamma z)$}
For a rational <matrix> $\gamma$ of positive <determinant>, use the positive real power of $\det\gamma$ in the displayed <slash operator for modular forms>. It satisfies $(f|_k\gamma)|_k\eta=f|_k(\gamma\eta)$ by the <automorphy factor> identity and multiplicativity of the <determinant>. It agrees with the usual operator on the <modular group>. The determinant factor is essential for the stated normalization of the <Hecke operators>.
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