Infinite Families of Simple Holomorphic Eta Quotients

TL;DR

This paper develops methods to construct simple holomorphic eta quotients at large prime power levels, extending known results beyond cubefree levels and impacting the understanding of their irreducibility.

Contribution

It introduces new constructions for simple holomorphic eta quotients at arbitrarily large prime power levels, expanding the class of known examples.

Findings

Constructed eta quotients for large prime power levels

Extended known results beyond cubefree levels

Implications for irreducibility of eta quotients

Abstract

We address the problem of constructing a simple holomor- phic eta quotient of a given level N . Such constructions are known for all cubefree N . Here, we provide such constructions for arbitrarily large prime power levels. As a consequence, we obtain an irreducibility