Abstract: Modular forms lie at the heart of number theory. They are simultaneously analytic and algebraic objects that encode deep arithmetic information. Their arithmetic content is encoded in the coefficients of their Fourier series. A major breakthrough in the analysis of Fourier coefficients of modular forms was the Hardy-Ramanujan (1918) asymptotic formula for the number of integer partitions. Their work was the first instance of the so-called "circle method" which was later used to determine the asymptotic growth of the Fourier coefficients for a broad class of modular forms. In this talk, we will describe some recent work to rederive these asymptotic estimates without using the circle method. These new methods may be simpler and require very little background in modular forms to understand. An application to the j invariant of elliptic curves will be a motivating example.