Quasimodular Forms and Vector-valued Modular Forms
In  Kuga and Shimura determined all holomorphic vector differential forms ω satisfying ω ◦ γ = ρ(γ)ω (10.1) for all γ ∈ Γ, where ρ is a symmetric tensor representation of a discrete subgroup Γ of SL(2,R). They constructed such a form corresponding to each modular form of weight ≤ n + 2 and showed that any holomorphic vector form satisfying (10.1) can be written as a sum of the vector forms associated to modular forms of weight ≤ n + 2.
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