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The character of an elliptic modular form $f$ of weight $k$ for the group $\Gamma$ is the Dirichlet character $\chi$ that appears in its transformation under the action of the defining group $\Gamma$. Namely, \[f(\gamma z) = \chi(d)(cz+d)^k f(z) \] for any $z\in\mathcal{H}$ and $\gamma = \begin{pmatrix} * & * \\ c & d \end{pmatrix}\in\Gamma$. Here $\Gamma$ is a subgroup of $\rm{SL}_2(\mathbb{Z})$ containing the principal congruence subgroup $\Gamma(N)$, and $\chi$ is a character mod $N$.

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  • Review status: reviewed
  • Last edited by David Farmer on 2019-04-09 22:57:32
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