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arXiv · 1404.4596

Twisting of Siegel paramodular forms

Jennifer Johnson-Leung·Brooks Roberts
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Abstract

Let $S_k(\Gamma^{\mathrm{para}}(N))$ be the space of Siegel paramodular forms of level $N$ and weight $k$. Let $p\nmid N$ and let $\chi$ be a nontrivial quadratic Dirichlet character mod $p$. Based on our previous work, we define a linear twisting map $\mathcal{T}_\chi:S_k(\Gamma^{\mathrm{para}}(N))\rightarrow S_k(\Gamma^{\mathrm{para}}(Np^4))$. We calculate an explicit expression for this twist and give the commutation relations of this map with the Hecke operators and Atkin-Lehner involution for primes $\ell\neq p$.

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Jennifer Johnson-Leung, Brooks Roberts. 2014-04-17. Twisting of Siegel paramodular forms. https://arxiv.org/abs/1404.4596

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