Abstract
The classical Maass Spezialschar is a Hecke-stable subspace of the level one
holomorphic Siegel modular forms of genus two, i.e., on $\mathrm{Sp}_4$, cut
out by certain linear relations between the Fourier coefficients. It is a
theorem of Andrianov, Maass, and Zagier, that the classical Maass Spezialschar
is exactly equal to the space of Saito-Kurokawa lifts. We study an analogous
space of quaternionic modular forms on split $\mathrm{SO}_8$, and prove the
analogue of the Andrianov-Maass-Zagier theorem. Our main tool for proving this
theorem is the development of a theory of a Fourier-Jacobi expansion of
quaternionic modular forms on orthogonal groups.