  We consider the Fourier expansion of a Hecke (resp.\ Hecke--Maa\ss) cusp form
of general level $N$ at the various cusps of $\Gamma_{0}(N)\bs\Hb$. We explain
how to compute these coefficients via the local theory of $p$-adic Whittaker
functions and establish a classical Vorono\"i summation formula allowing an
arbitrary additive twist. Our discussion has applications to bounding sums of
Fourier coefficients and understanding the (generalised) Atkin--Lehner
relations.
