A Jahn-Teller linear-plus-quadratic Hamiltonian is shown to account for nest of the observed band positions and intensities in the absorption and emission spectra of Ag3. Coupling parameters obtained for a simultaneous fit to absorption and emission results are k=1.93, g=0.25 for the E’ ground state and k=0.19, g=0.02 for the E" excited state. At higher vibrational energies, simple Jahn-Teller calculations predict fewer bands than observed. Calculations including spin-orbit coupling with larger linear coupling partially quenched by the Ham effect offer a reasonable explanation for this higher energy structure. Splittings and intensity sharing at lower vibrational energies, however, demand higher-order Jahn-Teller coupling, indicating the need for more extensive calculation simultaneously incorporating quadratic Jahn-Teller effects, spin-orbit coupling, and perhaps anharmonicity.