The Large-Eddy Simulation of a reduced-scale rocket engine operated by DLR has been conducted. This configuration features 42 coaxial injectors fed with liquid oxygen and gaseous hydrogen. For a given set of injection conditions the combustor exhibits strong transverse thermo-acoustic oscillations that are retrieved by the numerical simulation. The spatial structure of the two main modes observed in the LES is investigated through 3D Fourier analysis during the limit cycle. They are respectively associated with the first transverse and first radial resonant acoustic modes of the combustion chamber. The contributions of each individual flame to the unsteady heat release rate and the Rayleigh index are reconstructed for each mode. These contributions are in both cases low in the vicinity of velocity anti-nodes and high near pressure anti-nodes. Moreover it is noticed that these pressure fluctuations lead to large velocity oscillations in the hydrogen stream. From these observations, a driving mechanism for the flame response is proposed and values for the gain and phase of the associated flame transfer function are evaluated from the LES.