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

## TL;DR

This paper computes the generators and relations of graded rings of paramodular forms of degrees 2 at levels 5 and 7, using explicit constructions and restrictions to Humbert surfaces.

## Contribution

It provides explicit generators and relations for these rings, expressed via Gritsenko lifts and Borcherds products, advancing understanding of paramodular forms at these levels.

## Key findings

- Generators expressed as quotients of lifts and products
- Relations among generators explicitly computed
- Characterization of forms on Humbert surfaces used

## Abstract

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.