Although brain oscillations involving the basal ganglia (BG) have been the target of extensive research, the main focus lies disproportionally on oscillations generated within the BG circuit rather than other sources, such as cortical areas. We remedy this here by investigating the influence of various cortical frequency bands on the intrinsic effective connectivity of the BG, as well as the role of the latter in regulating cortical behaviour. To do this, we construct a detailed neural model of the complete BG circuit based on fine-tuned spiking neurons, with both electrical and chemical synapses as well as short-term plasticity between structures. As a measure of effective connectivity, we estimate information transfer between nuclei by means of transfer entropy. Our model successfully reproduces firing and oscillatory behaviour found in both the healthy and Parkinsonian BG. We found that, indeed, effective connectivity changes dramatically for different cortical frequency bands and phase offsets, which are able to modulate (or even block) information flow in the three major BG pathways. In particular, alpha (8-12Hz) and beta (13-30Hz) oscillations activate the direct BG pathway, and favour the modulation of the indirect and hyper-direct pathways via the subthalamic nucleus-globus pallidus loop. In contrast, gamma (30-90Hz) frequencies block the information flow from the cortex completely through activation of the indirect pathway. Finally, below alpha, all pathways decay gradually and the system gives rise to spontaneous activity generated in the globus pallidus. Our results indicate the existence of a multimodal gating mechanism at the level of the BG that can be entirely controlled by cortical oscillations, and provide evidence for the hypothesis of cortically-entrained but locally-generated subthalamic beta activity. These two findings suggest new insights into the pathophysiology of specific BG disorders.