This dataset includes the data on which the figures of the preprint "Floquet dynamics of ultracold atoms in optical lattices with a parametrically modulated trapping potential" by Usman Ali, Martin Holthaus, Torsten Meier ( https://arxiv.org/abs/2405.02125v1 ) are based and the relevant codes that were used to generate the data. U.A. gratefully acknowledges support from Deutscher Akademischer Austauschdienst (DAAD, German Academic Exchange Service) through a doctoral research grant and we thank the PC2 (Paderborn Center for Parallel Computing) for providing computing time. M.H. has been supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Project No. 397122187.