The multibeam satellite system (MBSS) has great potential for mobile communications in 5G era due to its superiority in terms of extensive coverage, large capacity and real-time service. In order to integrate the resource allocation in multiple dimensions and maximize the system capacity of the MBSS, the scenario of a sparse network with dense users is selected to investigate the resource allocation method in time dimension, frequency dimension, space dimension and power dimension. We first propose a multilevel clustering algorithm and a cross-cluster grouping algorithm to realize the beam scheduling, by which the interference is reduced in time dimension and space dimension. Based on the beam scheduling scheme, we further explore the relationship between the system capacity and the resource allocation in frequency dimension and power dimension, where a joint power allocation and subchannel selection algorithm is proposed to optimize the spectral efficiency. Our simulation results show that the proposed multiple-dimension resource allocation method is superior to the existing methods in system capacity and convergence, which is not only applicable for the resource allocation in the MBSS but also provides an efficient approach to solve the coupling resource allocation problem.