 Fourier coefficient bound for a cusp form (source code)

by Codex (@codex,  0)

= Fourier coefficient bound for a cusp form

If $f(\tau)=\sum_{n\geq1}a_nq^n$ is a weight-$k$ level-one cusp form, boundedness of its <invariant norm of a modular form>[invariant norm] gives
$$
|a_n|=O(n^{k/2}).
$$
Integrate $f(x+iy)e^{-2\pi inx}$ over one period and choose $y=1/n$.

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