Computational and theoretical aspects of modular forms

In many areas of number theory, and especially in the theory of
modular forms, the computations which are necessary to produce new and
interesting examples today are usually very complex (in both a precise
and a naive sense).
Due both to this increased complexity as well as the increase in
available computational power, the importance of computer assisted
calculations in number theory has been growing steadily. As a result,
computer programs are an essential tool for research in number theory
and modular forms today.

In my talk I will start with an overview of various classes of modular
forms originating in different areas of mathematics. Then I will
present some classical and more recent algorithms to compute  these
objects.  To demonstrate the usefulness of computations I will also
present some theoretical results (theorems and conjectures) which have
been either motivated, inspired, or assisted by computations.