In this talk, we first give a quick introduction to elliptic modular forms with various examples focusing on the applications of dimension formulas. Then we will report some recent results on dimension formulas of Siegel modular forms of degree 2. In particular, we will describe how to use local and global representation theory of the algebraic group GSp(4) to obtain new dimension formulas of certain families of Siegel modular forms of degree 2. Finally, we will also discuss some applications of this kind of dimensional data to other related topics in number theory. This is partially joint work with Manami Roy and Ralf Schmidt.