The dimensions of spaces of holomorphic second-order automorphic forms and their cohomology
arXiv:math/0411135
Abstract
Second-order automorphic forms are similar to the usual automorphic forms but have a weaker automorphy condition. We answer a question of Zagier and find the dimensions of spaces of holomorphic, even weight, second-order forms. We also establish a cohomological interpretation.
v2. Very minor changes. 35 pages