the classical spezialschar is the subspace of the space of holomorphic modular forms on  $\mathrm{sp}_4(\mathbb{z})$ whose fourier coefficients satisfy a particular system of linear equations. an equivalent characterization of the spezialschar can be obtained by combining work of maass, andrianov, and zagier, whose work identifies the spezialschar in terms of a theta-lift from $\widetilde{\mathrm{sl}_2}$. inspired by work of gan-gross-savin, weissman and pollack have developed a theory of modular forms on the split adjoint group of type d_4. in this setting we describe an analogue of the classical spezialschar, in which fourier coefficients are used to characterize those modular forms which arise as theta lifts from holomorphic forms on $\mathrm{sp}_4(\mathbb{z})$.