Nonadiabatic molecular dynamics simulations are used to analyze the role of different solvent molecular degrees of freedom in the nonradiative relaxation of the first excited state of the hydrated electron. The relaxation occurs through a spatially diffuse multimode coupling between the adiabatic electronic states, indicating that the process cannot be described by a single-mode promotion model frequently used in the "large molecule" limit of gas phase theories. Solvent librations and vibrations, and the H2O asymmetric stretch in particular, are found to be the most effective promoters of the electronic transition. Dissipation of the released energy to the solvent proceeds on two time scales : a fast 10-20 fs heating of the first solvation shell, where most of the energy is accepted by the librational degrees of freedom, and a several hundred femtosecond global reconstruction of the solvent as the first shell transfers its excess energy to the rest of the molecules. The implications of our use of a semiclassical approximation as the criterion for good promoting and energy dissipating modes are discussed.