The dimensions of spaces of holomorphic second-order automorphic forms   and their cohomology
  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. 
Nikolaos Diamantis, Cormac O'Sullivan