Fourier coefficients of vector-valued modular forms of dimension 2

Cameron Franc; Geoffrey Mason

doi:10.4153/CMB-2014-007-3

Fourier coefficients of vector-valued modular forms of dimension 2

Number Theory 2019-08-15 v1

Authors: Cameron Franc , Geoffrey Mason

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Abstract

We prove the following theorem. Suppose that $F=(f_1, f_2)$ is a 2-dimensional vector-valued modular form on $SL_2(Z)$ 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.

Keywords

vector-valued modular forms Fourier coefficients congruence subgroup rational coefficients modular group

Cite

@article{arxiv.1304.4288,
  title  = {Fourier coefficients of vector-valued modular forms of dimension 2},
  author = {Cameron Franc and Geoffrey Mason},
  journal= {arXiv preprint arXiv:1304.4288},
  year   = {2019}
}

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