  Dedekind symbols generalize the classical Dedekind sums (symbols). The
symbols are determined uniquely by their reciprocity laws up to an additive
constant. There is a natural isomorphism between the space of Dedekind symbols
with polynomial (Laurent polynomial) reciprocity laws and the space of cusp
(modular) forms. In this article we introduce Hecke operators on the space of
weighted Dedekind symbols. We prove that these newly introduced operators are
compatible with Hecke operators on the space of modular forms. As an
application, we present formulae to give Fourier coefficients of Hecke
eigenforms. In particular we give explicit formulae for generalized Ramanujan's
tau functions.
