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Oscillations occurring simultaneously in a given area represent a physiological unit of brain states. They allow for temporal segmentation of spikes and support distinct behaviors. To establish how multiple oscillatory components co-vary simultaneously and influence neuronal firing during sleep and wakefulness in mice, we describe a multivariate analytical framework for constructing the state space of hippocampal oscillations. Examining the co-occurrence patterns of oscillations on the state space, across species, uncovered the presence of network constraints and distinct set of cross-frequency interactions during wakefulness compared to sleep. We demonstrated how the state space can be used as a canvas to map the neural firing and found that distinct neurons during navigation were tuned to different sets of simultaneously occurring oscillations during sleep. This multivariate analytical framework provides a window to move beyond classical bivariate pipelines for investigating oscillations and neuronal firing, thereby allowing to factor-in the complexity of oscillation–population interactions.