Conformal Characters and Theta Series

TL;DR

This paper constructs vector valued modular forms using theta series and applies this framework to derive explicit formulas for conformal characters in rational W-algebra models.

Contribution

It introduces a method to express conformal characters of W-algebras as theta series-based modular forms, providing computationally accessible formulas.

Findings

Explicit formulas for conformal characters derived

Method for constructing vector valued modular forms established

Application to rational W-algebra models demonstrated

Abstract

We describe the construction of vector valued modular forms transforming under a given congruence representation of the modular group SL(2,Z) in terms of theta series. We apply this general setup to obtain closed and easily computable formulas for conformal characters of rational models of W-algebras.