The Classification of Higher Order Modular Forms and their Cohomology

TL;DR

This paper constructs bases for higher order modular forms across all weights and orders, and offers a cohomological interpretation, advancing the understanding of their structure and relationships.

Contribution

It introduces a comprehensive basis construction for higher order modular forms and links them to cohomology, providing new tools for their analysis.

Findings

Established bases for all higher order modular forms.

Provided a cohomological framework for these forms.

Enhanced understanding of their structural properties.

Abstract

We construct bases for the spaces of higher order modular forms of all orders and weights. We also provide a cohomological interpretation of these forms.