The human brain is a complex system, whose activity exhibits flexible and continuous reorganization across space and time. The decomposition of whole-brain recordings into harmonic modes has revealed a repertoire of gradient-like activity patterns associated with distinct brain functions. However, the way these activity patterns are expressed over time with their changes in various brain states remains unclear. Here, we investigate healthy participants taking the serotonergic psychedelic -dimethyltryptamine (DMT) with the Harmonic Decomposition of Spacetime (HADES) framework that can characterize how different harmonic modes defined in space are expressed over time. HADES demonstrates significant decreases in contributions across most low-frequency harmonic modes in the DMT-induced brain state. When normalizing the contributions by condition (DMT and non-DMT), we detect a decrease specifically in the second functional harmonic, which represents the uni- to transmodal functional hierarchy of the brain, supporting the leading hypothesis that functional hierarchy is changed in psychedelics. Moreover, HADES' dynamic spacetime measures of fractional occupancy, life time and latent space provide a precise description of the significant changes of the spacetime hierarchical organization of brain activity in the psychedelic state.