Abelian approach to modular forms of neat 2-ball lattices: Dimension formulas

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 13

MSC 2000

11G15 Complex multiplication and moduli of abelian varieties

11G18 Arithmetic aspects of modular and Shimura varieties

14H52 Elliptic curves

14J25 Special surfaces

20H05 Unimodular groups, congruence subgroups

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.

Keywords:algebraic surfaces, Shimura varieties, arithmetic groups, Picard modular groups, unit ball, modular forms