  We investigate the electronic and vibrational spectra of SrTiO$_3$, as well
as the coupling between them, using first-principles calculations. We compute
electron-phonon scattering rates for the three lowest-energy conduction bands
and use Boltzmann transport theory to calculate the room-temperature mobility
of SrTiO$_3$. The results agree with experiment and highlight the strong impact
of longitudinal optical phonon scattering. Our analysis provides important
insights into the key factors that determine room temperature mobility, such as
the number of conduction bands and the nature and frequencies of longitudinal
phonons. Such insights provide routes to engineering materials with enhanced
mobilities.
