We present an extensive neutron scattering study on the ester methyl dynamics of poly(methyl methacrylate) (PMMA) in the temperature range from 1 to 200 K. The crossover from quantum tunneling to classical hopping has been investigated in an energy window from 0.5 mu eV to 2 meV. Inclastic measurements of the librational levels have been performed in the millielectronvolt range. The results have been analyzed in terms of a model that considers a Gaussian distribution of potential barriers for methyl group rotation. A 6-fold correction to the main 3-fold term of the potential has been added to get a good description of the librational peak. This distribution of mixed-symmetry barriers gives an excellent description of the spectra in the whole temperature range.