Fourier coefficients of vector-valued modular forms of dimension 2

Cameron Franc; Geoffrey Mason

doi:10.4153/cmb-2014-007-3

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arXiv · 1304.4288

Fourier coefficients of vector-valued modular forms of dimension 2

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.

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BibTeX RIS

Cameron Franc, Geoffrey Mason. 2013-04-15. Fourier coefficients of vector-valued modular forms of dimension 2. https://doi.org/10.4153/cmb-2014-007-3

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