A supercharacter theory for PSL(2,q) and SO(3,q)

The concept of a supercharacter theory for a finite group was introduced in 2008 by Diaconis and Iasaacs in [6]. In their article the notion of irreducible characters and conjugacy classes is generalized to superchacters and superclasses while still maintaining important information about the group. This article continues an investigation of a specific supercharacter theory where the supercharacters are taken to be sums of irreducible characters of the same degree. We show this supercharacter theory construction can be done for all projective special linear groups PSL(2,q) and all special orthogonal groups SO(3,q) where q is any power of an (even or odd) prime.