Abstract view
Fourier Coefficients of Vectorvalued Modular Forms of Dimension $2$


Published:20140405
Printed: Sep 2014
Cameron Franc,
Department of Mathematics, University of California, Santa Cruz
Geoffrey Mason,
Department of Mathematics, University of California, Santa Cruz
Abstract
We prove the following Theorem. Suppose that $F=(f_1, f_2)$ is a $2$dimensional vectorvalued modular form
on $\operatorname{SL}_2(\mathbb{Z})$ 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.