## STNB2022 (35th edition)

### Computing Paramodular forms using Quinary modular forms

Ariel Pacetti

#### Abstract

Computing tables of modular forms is a major challenge in number theory. For classical modular forms there are mainly two different approaches to compute such tables, namely via the use of modular symbols, or via the use of (ternary or quaternary) quadratic forms. In the present talk we will explain how one can extend the classical approach using a Hecke isomorphism between the space of siegel paramodular forms of weight (k,j) for $k \ge 3$ and a subspace of algebraic quinary modular forms (for an explicit choice of a lattice). The existence of Yoshida lifts in the space of algebraic quinary modular forms, allows us to prove different types of congruences predicted by Harder and a congruence predicted by Buzzard and Golyshev.