Fourier coefficients of vector-valued modular forms of dimension 2
Abstract
We prove the following theorem. Suppose that F=(f1, f2) is a 2-dimensional vector-valued modular form on SL2(Z) whose component functions f1, f2 have rational Fourier coefficients with bounded denominators. Then f1 and f2 are classical modular forms on a congruence subgroup of the modular group.
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