Abelian approach to modular forms of neat 2-ball lattices

Abstract

In previous papers [HoEis], [Ho2000] we found neat Picard modular surfaces with abelian minimal model and, conversely, a divisor criterion on abelian surfaces A for such a situation. For the corresponding ball lattices Gamma we prove dimension formulas for modular forms depending only on the intersection graph of the image on A of the compactification divisor of the Gamma-quotient surface.