Fourier coefficients of vector-valued modular forms of dimension 2

Abstract

We prove the following theorem. Suppose that $F=(f_1,f_2)$ is a 2-dimensional vector-valued modular form on $S{L}_2(Z)$ whose component functions $f_1,f_2$ have rational Fourier coefficients with bounded denominators. Then $f_1$ and $f_2$ are classical modular forms on a congruence subgroup of the modular group.

References in corpus (1)

• Structure of the module of vector-valued modular forms

Cited by in corpus (7)

• Vertex operator algebras, Higgs branches, and modular differential equations
• Discreteness and Integrality in Conformal Field Theory
• Classification of some vertex operator algebras of rank 3
• Classification of extremal vertex operator algebras with two simple modules
• The arithmetic of vector-valued modular forms on ${\Gamma }_0(2)$
• Quasimodular forms as solutions of Modular differential equations
• Two approaches to the holomorphic modular bootstrap