Quinary forms and paramodular forms
Heilbronn Number Theory Seminar
17th November 2021, 4:00 pm – 5:00 pm
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,
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).