Let \(F\) be a Siegel cusp form of weight \(k\in \mathbb{Z}\) and degree 2 for the full Siegel modular group, and assume that \(F\) is an eigenform of all Hecke operators \(T_2(n)\) with eigenvalue \(\lambda(n)\). The author proves: \(F\) belongs to the Maaß space (“Spezialschar”) if and only if \(\lambda(n)> 0\) for all \(n\in \mathbb{N}\).