On Level One Cuspidal Bianchi Modular Forms

TL;DR

This paper reports extensive computational results identifying rare level one cuspidal Bianchi modular forms that are not derived from elliptic modular forms, expanding understanding of these special automorphic forms.

Contribution

It provides the first large-scale computational evidence of non-lift cuspidal Bianchi modular forms at level one.

Findings

Discovered several new non-lift cuspidal Bianchi modular forms

Confirmed rarity of such forms at level one

Enhanced data on Bianchi modular forms through extensive calculations

Abstract

In this paper, we present the outcome of vast computer calculations, locating several of the very rare instances of level one cuspidal Bianchi modular forms that are not lifts of elliptic modular forms.