  We show that Fourier coefficients of automorphic forms attached to minimal or
next-to-minimal automorphic representations of ${\mathrm{SL}}_n(\mathbb{A})$
are completely determined by certain highly degenerate Whittaker coefficients.
We give an explicit formula for the Fourier expansion, analogously to the
Piatetski-Shapiro-Shalika formula. In addition, we derive expressions for
Fourier coefficients associated to all maximal parabolic subgroups. These
results have potential applications for scattering amplitudes in string theory.
