We report quantum calculations of vibrational states of trans N-methyl acetamide (H3C-HNCO-CH3) in full dimensionality using the code MULTIMODE. In this code, the full potential is represented as a hierarchical sum of n-mode potentials in the normal coordinates. All 30 one- and 435 two-mode potentials are included in the sum, as well as a restricted set of 10 three-mode potentials corresponding to the experimentally probed amide band. The electronic energies on the various n-mode grids are obtained using ab initio Moller-Plesset perturbation theory with a triple-zeta quality, correlation-consistent basis set. Convergence tests of the low-lying vibrational eigenvalues of the amide band show that this limited three-mode representation of the full potential yields well converged results that are in excellent agreement with experiment. The infrared spectrum in the region of the amide bands is calculated and also agrees well with experiment.