We describe a characterization for the Maaß space associated with the paramodular group of degree and square-free level . As an application we show that the Maaß space is invariant under all Hecke operators. As a consequence, we conclude that the associated Siegel–Eisenstein series belongs to the Maaß space.
"The Maaß space for paramodular groups." Kyoto J. Math. 60 (4) 1191 - 1207, December 2020. https://doi.org/10.1215/21562261-2019-0058