Weight of a Siegel modular form (awaiting review)

The weight of a Siegel modular form $f$ of degree g is the finite-dimensional complex representation $\rho$ of $\GL(g,\mathbb{C})$ 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 Siegel upper half space $\mathcal{H}_g$. That is, the weight is the representation $\rho$ in the transformation law $$ f\left( (a \tau + b)(c \tau + d)^{-1} \right) = \rho(c \tau + d) f(\tau) . $$

Irreducible representations of $\GL(g,\mathbb{C})$ are indexed by their highest weight.