### Quinary forms and paramodular forms

Heilbronn Number Theory Seminar

17th November 2021, 4:00 pm – 5:00 pm

, online

The goal of this talk is to explain how one can use orthogonal modular

forms to find and prove congruences between paramodular forms.

In the first part of the talk I will give a brief review of orthogonal

modular forms and how the case of SO(5) can be used to compute

paramodular forms, based on recent work of Rama-T, Rösner-Weissauer,

Dummigan-Pacetti-Rama-T.

In the second part of the talk I will explain how we use orthogonal

modular forms to prove congruences of paramodular forms, including

examples of Fretwell and of Golyshev. A key ingredient for this is

the unexpected appearance of orthogonal eigenforms which /do not/

correspond to paramodular forms (see Rama-T in ANTS 2020).

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