A note on traces of singular moduli

TL;DR

This paper generalizes previous work on congruences related to traces of singular moduli, expanding the scope to include Hauptmodul associated with higher level genus zero groups.

Contribution

It introduces a broader framework for congruences of traces of singular moduli linked to higher level genus zero groups.

Findings

Extended congruence relations for traces of singular moduli.

Generalized Osburn's results to higher level groups.

Established new connections between Hauptmodul and singular moduli.

Abstract

We will generalize Osburn's work about a congruence for traces defined in terms of Hauptmodul associated to certain genus zero groups of higher levels.