Bianchi modular forms

Appears in collection : Summer School 2022 - Cohomology, Geometry and Explicit number theory (COGENT)

Bianchi Modular Forms are generalizations of classical modular forms for imaginary quadratic fields. Similar to the classical case, we can use the theory of modular symbols for computation. However, when the class group of the field is non-trivial, we can only compute certain components of the modular form. However, we can use techniques developed by Cremona and his students to extract the Bianchi Modular forms as Hecke eigensystems. In this talk, I will go over some of these computational techniques for the field $\mathbb{Q}(\sqrt{-17})$ which has class number $4$.