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Invariant norm of a modular 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 $y=1/n$.

Fourier coefficient bound for a cusp form

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 137 / 2 / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 137 / 1 / b / Solution

Fourier coefficient bound for a cusp form

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Fourier coefficient bound for a cusp form

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