Modular forms and applications to coding theory

Michael Figelius (Seigen)

Abstract

Modular forms are complex valued functions on the upper half plane, which have a power series expansion. They are of high interest in pure mathematics. Not only are they interesting in their own right, they also have applications in number theory, geometry, quantum field theory, cryptography, coding theory and many more areas.

We will give an overview on what a modular form actually looks like and we will present a nice way to construct weight 2 modular forms for some congruence subgroups by hand using Manin's approach. Modulo a prime p one ends up with linear codes, which we studied and obtained several properties related to vector spaces of modular forms.