Abstract
We study the graded space ℋ(ρ) of holomorphic vector-valued modular forms of integral weight associated to a 2-dimensional irreducible representation ρ of SL(2,ℤ). When ρ(T) is unitary, a complete description of ℋ(ρ) is given: the Poincaré series is calculated and it is shown that ℋ(ρ) is a free module of rank 2 over the ring of (classical) holomorphic modular forms on SL(2,ℤ).
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Supported by the NSA, the NSF and the Committee on Research at the University of California, Santa Cruz.
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Mason, G. 2-Dimensional vector-valued modular forms. Ramanujan J 17, 405–427 (2008). https://doi.org/10.1007/s11139-007-9054-4
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DOI: https://doi.org/10.1007/s11139-007-9054-4