GABAergic inhibitory Fast Spiking (FS) basket cells (BCs) are recognized for their integral role in shaping learning and memory. This study delves into the orchestration of these processes by FS BCs, particularly their involvement in controlling hippocampal high-frequency gamma oscillations (80-200 Hz) coupled with theta oscillatory activity (3-10 Hz). While existing research predominantly explores the connectivity of these neurons during memory-related rhythms, our investigation highlights an additional layer of subcellular complexity. Recent modeling and experimental findings reveal that FS BCs boast two distinct flavors of nonlinear dendrites: the supralinear, generating local dendritic spikes, and the sublinear. Our hypothesis posits that the activation of these nonlinear dendrites may manifest at the neural circuit level by modulating theta-gamma oscillations. To scrutinize this hypothesis, we constructed a biologically plausible hippocampal microcircuit model. This model encompasses populations of pyramidal and FS BCs, calibrated with in vitro electrophysiological data. Subsequently, we subjected the network to theta-like input, observing the successful reproduction of theta-nested high gamma activity at the local field potential (LFP) level. Through a diverse array of simulation protocols, we present a groundbreaking prediction: supralinear and sublinear FS BCs dendrites differentially modulate the excitation-to-inhibition balance. This modulation, in turn, results in variations in the power and frequency features of the coupled oscillatory activity. Our preliminary results underscore the transformative impact of subcellular dendritic nonlinear features of interneurons on hippocampal oscillations and open avenues for further exploration into the nuanced role of FS BCs dendritic computations in shaping cognitive processes at the neural circuit level.