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

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