The dimension of vector-valued modular forms of integer weight
P. Bantay

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.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory
