Congruences satisfied by eta-quotients

TL;DR

This paper presents an algorithm to explicitly compute congruences satisfied by eta-quotients, extending known results about modular forms and partition functions, with practical examples demonstrating its effectiveness.

Contribution

The paper introduces a new algorithm for explicitly finding congruences of eta-quotients, advancing computational methods in modular forms.

Findings

Algorithm successfully computes explicit congruences.

Examples illustrate the method's applicability.

Extends previous theoretical results to practical computations.

Abstract

The values of the partition function, and more generally the Fourier coefficients of many modular forms, are known to satisfy certain congruences. Results given by Ahlgren and Ono for the partition function and by Treneer for more general Fourier coefficients state the existence of infinitely many families of congruences. In this article we give an algorithm for computing explicit instances of such congruences for eta-quotients. We illustrate our method with a few examples.