Weight of an elliptic modular form (reviewed)

The weight of an elliptic modular form $f$ is the integer or half-integer power of $(cz+d)$ that occurs in the modular transformation property of $f$ under the action of $\gamma = \left( \begin{array}{ll} a & b \\ c & d \end{array}\right)$ on the upper half plane. That is, the weight is the number $k$ in the transformation law $$ f\left( \frac{a z + b}{c z + d} \right) = \chi(d)(c z + d)^k f(z) . $$