I'm currently writing my master thesis about the j-invariant and his q-expansion. Now i have the result that the growth of the coefficients is asymptotically $$c(n) \sim \frac{e^{4\pi \sqrt{n}}}{\sqrt{2}n^{\frac{3}{4}}}.$$

Is there any special reason to investigate this growth? Is it possible to use this result to make some statements about the j-invariant or is this just a "nice-to-know" information?

Thanks in advance.