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Let denote a finite index subgroup of the modular group and let denote a finite-dimensional complex representation of Let denote the collection of holomorphic vector-valued modular forms for and let denote the collection of modular forms on . Then is a -graded -module. It has been proven that may not be projective as a -module. We prove that is Cohen-Macaulay as a -module. We also explain how to apply this result to prove that if is a polynomial ring, then is a free...
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