Communications in Number Theory and Physics

Volume 9 (2015)

Number 2

Fourier coefficients of three-dimensional vector-valued modular forms

Pages: 387 – 411



Christopher Marks (Department of Mathematics and Statistics, California State University, Chico, Calif., U.S.A.)


We prove that only a finite number of three-dimensional, irreducible representations of the modular group admit vector-valued modular forms with bounded denominators. This provides a verification, in the three-dimensional setting, of a conjecture concerning the Fourier coefficients of noncongruence modular forms, and reinforces the understanding from mathematical physics that when such a representation arises in rational conformal field theory, its kernel should be a congruence subgroup of the modular group.

2010 Mathematics Subject Classification

11F30, 11F99

Published 12 June 2015