The dimension of vector-valued modular forms of integer weight

TL;DR

This paper derives a dimension formula for vector-valued modular forms of integer weight with finite image multiplier systems, analyzing generator weights and duality relations between forms.

Contribution

It provides a new explicit dimension formula and explores the structure and duality properties of vector-valued modular forms.

Findings

Dimension formula for vector-valued modular forms established

Analysis of weight distribution of module generators

Duality relation between cusp and holomorphic forms demonstrated

Abstract

We present a dimension formula for spaces of vector-valued modular forms of integer weight in case the associated multiplier system has finite image, and discuss the weight distribution of the module generators of holomorphic and cusp forms, as well as the duality relation between cusp forms and holomorphic forms for the contragredient.