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The weight of a Siegel modular form $f$ of degree 2 is the pair of non-negative integers 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 $\mathcal{H}_2$. That is, the weight is the numbers $(k,j)$ in the transformation law $$ f\left( (a \tau + b)(c \tau + d)^{-1} \right) = \det(c \tau + d)^k {\rm Sym}^j(c \tau + d) f(\tau) . $$

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  • Review status: beta
  • Last edited by Eran Assaf on 2022-08-31 09:35:16
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