Structure of the module of vector-valued modular forms
Let V be a representation of the modular group Γ of dimension p. We show that the ℤ-graded space ℋ(V) of holomorphic vector-valued modular forms associated to V is a free module of rank p over the algebra ℳ of classical holomorphic modular forms. We study the nature of ℋ considered as a functor from...
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| Veröffentlicht in: | Journal of the London Mathematical Society 2010-08, Vol.82 (1), p.32-48 |
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| container_title | Journal of the London Mathematical Society |
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| creator | Marks, Christopher Mason, Geoffrey |
| description | Let V be a representation of the modular group Γ of dimension p. We show that the ℤ-graded space ℋ(V) of holomorphic vector-valued modular forms associated to V is a free module of rank p over the algebra ℳ of classical holomorphic modular forms. We study the nature of ℋ considered as a functor from Γ-modules to graded ℳ-lattices and give some applications, including the calculation of the Hilbert–Poincaré series of ℋ(V) in some cases. |
| doi_str_mv | 10.1112/jlms/jdq020 |
| format | Article |
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| language | eng |
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| source | Wiley Online Library Journals Frontfile Complete; Alma/SFX Local Collection |
| title | Structure of the module of vector-valued modular forms |
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