Class invariants for certain non-holomorphic modular functions

TL;DR

This paper explores class polynomials for non-holomorphic modular functions from negative weight forms, providing conditions for irreducibility and enabling the generation of numerous new class invariants.

Contribution

It introduces general irreducibility conditions for class polynomials of non-holomorphic modular functions, expanding the set of known class invariants.

Findings

Established criteria for irreducibility of class polynomials

Generated infinitely many new class invariants

Extended prior work on modular forms of negative weight

Abstract

Inspired by prior work of Bruinier and Ono and Mertens and Rolen, we study class polynomials for non-holomorphic modular functions arising from modular forms of negative weight. In particular, we give general conditions for the irreducibility of class polynomials. This allows us to easily generate infintely many new class invariants.