This work considers a theoretical approach to analyzing receptivity of a realistic geometry in hypersonic flow to a freestream entropy disturbance. Receptivity coefficients and phase angles are determined at a variety of locations by applying multimode decomposition to direct numerical simulation (DNS) data. The multimode decomposition scheme is implemented and rigorous verification performed against results from previous works. The method is then applied to the DNS results characterized by a freestream hotspot perturbation interacting with the bow-shock of Purdue's blunt compression cone in a Mach-6 freestream. The DNS data is decomposed into elements of the discrete and continuous spectra at various locations and frequencies, and the results compared to a prior, qualitative LST analysis. The previous analysis' conclusions are confirmed, showing that in the region downstream of the mode F / S synchronization location for the most unstable frequency, mode S is amplified and becomes the dominant mechanism of transition. The results upstream of this location are shown to be dominated by low frequency mode F perturbations. Receptivity coefficients are computed and examined for the branch I/II neutral frequencies at several locations. Brief continuous spectrum analysis is performed, showing agreement with previous work in the limited contribution from the entropy and vorticity spectra.