Modular forms on SU(2,1) with weight $\frac{1}{3}$

TL;DR

This paper introduces new examples of holomorphic modular forms on SU(2,1) with fractional weight 1/3 and proposes a method to identify levels where such forms can be found.

Contribution

It provides the first known examples of fractional weight modular forms on SU(2,1) and a systematic approach to determine their levels.

Findings

New examples of fractional weight modular forms on SU(2,1)

A method for predicting levels of such forms

Insights into the structure of modular forms with fractional weights

Abstract

In this note, we describe several new examples of holomorphic modular forms on the group SU(2,1). These forms are distinguished by having weight $\frac{1}{3}$. We also describe a method for determining the levels at which one should expect to find such fractional weight forms.