Modularity experiments on $S_4$-symmetric double octics

TL;DR

This paper explores the modularity of double octic threefolds with $S_4$ symmetry, using extensive computational experiments to identify connections to weight four modular forms.

Contribution

It introduces a large-scale computational approach to discover double octic threefolds linked to modular forms, focusing on $S_4$ symmetry.

Findings

Identification of new double octic threefolds related to modular forms

Insights into the structure of $S_4$-symmetric geometries

Potential classification of modularity in these varieties

Abstract

We will invest quite some computer power to find double octic threefolds that are connected to weight four modular forms.