ABSTRACT
The Hecke operator Tp is the linear map defined on formal power series, such as
E(q) = ∞∑
a(n)qn,
by
(E|Tp)(q) def= ∞∑
a(np)qn + χ(p) ∞∑
a(n)qpn.
(E|Tp)(q) = (1 + χ(p))E(q).
In this chapter we will discuss four classical examples that are intended to serve as an indication of the basic questions treated in the theory of modular forms and their connection with number theory.
