The dimensions of spaces of holomorphic second-order automorphic forms and their cohomology

Diamantis, Nikolaos; O’Sullivan, Cormac

doi:10.1090/S0002-9947-08-04755-7

The dimensions of spaces of holomorphic second-order automorphic forms and their cohomology
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Trans. Amer. Math. Soc. 360 (2008), 5629-5666 Request permission

Abstract:

In this paper we answer a question of Zagier and find the dimensions of spaces of holomorphic second-order forms of even weight. We also establish a cohomological interpretation and prove an Eichler-Shimura-type isomorphism.

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