  In this paper, we consider automorphic forms on
$\mathrm{Sp}_4(\mathbb{A}_\mathbb{Q})$ which generate large discrete series
representations of $\mathrm{Sp}_4(\mathbb{R})$ as
$(\mathfrak{sp}_4(\mathbb{R}),K_\infty)$-modules. We determine the cuspidal
components and the structure of the space of such automorphic forms.
