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Graded rings of paramodular forms of levels $5$ and $7$

We compute generators and relations for the graded rings of paramodular forms of degree two and levels 5 and 7. The generators are expressed as quotients of Gritsenko lifts and Borcherds products. The computation is made possible by a characterization of modular forms on the Humbert surfaces of discriminant 4 that arise from paramodular forms by restriction.

preprint2020arXivOpen access
Brandon Williams
math.NT
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Brandon Williams

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