Geodesic
Fourier Coefficients of Vector-valued Modular Forms of Dimension 2
Canadian mathematical bulletin, Tome 57 (2014) no. 3, pp. 485-494

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DOI

We prove the following theorem. Suppose that $F\,=\,\left( {{f}_{1}},\,{{f}_{2}} \right)$ is a 2-dimensional, vector-valued modular form on $\text{S}{{\text{L}}_{2}}\left( \mathbb{Z} \right)$ 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.
DOI : 10.4153/CMB-2014-007-3
Mots-clés : 11F41, 11G99, vector-valued modular form, modular group, bounded denominators 
Franc, Cameron; Mason, Geoffrey. Fourier Coefficients of Vector-valued Modular Forms of Dimension 2. Canadian mathematical bulletin, Tome 57 (2014) no. 3, pp. 485-494. doi: 10.4153/CMB-2014-007-3
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