Here are some suggestions for topics for your paper. It’s not required to pick one of these; you can certainly pick something else if you like.
Modular forms and theta functions.
Ramanujan graphs and their applications.
Modular symbols.
The trace formula.
Quaternion algebras and compact quotients of the upper half plane.
The Langlands program.
Dimension formulas.
The Bruhat-Tits building and Hecke operators.
Siegel modular forms.
Hilbert modular forms.
Bianchi modular forms.
The modularity theorem and elliptic curves.