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Irreducible vector-valued modular forms of dimension less than six. (English) Zbl 1343.11052

Summary: An algebraic classification is given for spaces of holomorphic vector-valued modular forms of arbitrary real weight and multiplier system, associated to irreducible, \(T\)-unitarizable representations of the full modular group, of dimension less than six. For representations of dimension less than four, it is shown that the associated space of vector-valued modular forms is a cyclic module over a certain skew polynomial ring of differential operators. For dimensions four and five, a complete list of possible Hilbert-Poincaré series is given, using the fact that the space of vector-valued modular forms is a free module over the ring of classical modular forms for the full modular group. A mild restriction is then placed on the class of representation considered in these dimensions, and this again yields an explicit determination of the associated Hilbert-Poincaré series.

MSC:

11F55 Other groups and their modular and automorphic forms (several variables)
11F99 Discontinuous groups and automorphic forms
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References:

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