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

Cuspidal components of Siegel modular forms for large discrete series representations of $\mathrm{Sp}_4(\mathbb{R})$