On modular forms of weight 2 and representations of PSL(2, Z / pZ)

TL;DR

This paper revisits Hecke's 1930 work, explaining the relationship between class numbers of quadratic fields and representations of PSL(2, Z/pZ) on holomorphic differentials, emphasizing modular forms of weight 2.

Contribution

It provides an accessible translation and explanation of Hecke's original results connecting class numbers and group representations.

Findings

Established a relation between class number h(-q) and PSL(2, Z/pZ) representations

Clarified the role of modular forms of weight 2 in this context

Connected classical number theory with modular form theory

Abstract

This is essentially a translated (and explained) version of a peper Hecke published in 1930 where he shows, for a prime q, a relation between the class number h(-q) and the representation of PSL(2, Z / pZ) on the space of holomorphic differentials of X(q).