A Computational Study of the Asymptotic Behaviour of Coefficient Fields of Modular Forms

TL;DR

This paper presents computational analysis of the asymptotic behavior of coefficient fields of modular forms, revealing patterns that warrant further investigation into their arithmetic properties.

Contribution

It introduces large-scale computer calculations to explore the asymptotic properties of coefficient fields of modular forms, highlighting observed patterns.

Findings

Identification of patterns in coefficient fields

Computational evidence supporting conjectures

Foundation for future theoretical work

Abstract

The article motivates, presents and describes large computer calculations concerning the asymptotic behaviour of arithmetic properties of coefficient fields of modular forms. The observations suggest certain patterns, which deserve further study.