Normalizer Maps Modulo N

Abstract

The present paper is devoted to studying the maps corresponding to the suborbital graphs for the normalizer ΓB(N) of Γ0(N) modulo N, where N denotes a positive integer. We reveal the complete structure of these maps, finding their vertices, edges, darts, and faces explicitly. The maps we investigated in the present paper were all regular maps of large genus except for some low values of N.