Suppose that
$G$
is a simple reductive group over
$\mathbf{Q}$
, with an exceptional Dynkin type and with
$G(\mathbf{R})$
quaternionic (in the sense of Gross–Wallach). In a previous paper, we gave an explicit form of the Fourier expansion of modular forms on
$G$
along the unipotent radical of the Heisenberg parabolic. In this paper, we give the Fourier expansion of the minimal modular form
$\unicode[STIX]{x1D703}_{Gan}$
on quaternionic
$E_{8}$
and some applications. The
$Sym^{8}(V_{2})$
-valued automorphic function
$\unicode[STIX]{x1D703}_{Gan}$
is a weight 4, level one modular form on
$E_{8}$
, which has been studied by Gan. The applications we give are the construction of special modular forms on quaternionic
$E_{7},E_{6}$
and
$G_{2}$
. We also discuss a family of degenerate Heisenberg Eisenstein series on the groups
$G$
, which may be thought of as an analogue to the quaternionic exceptional groups of the holomorphic Siegel Eisenstein series on the groups
$\operatorname{GSp}_{2n}$
.
Derived Picard Groups of Preprojective Algebras of Dynkin Type