An event-based partial wave analysis (PWA) of the reaction γp→pω has been performed on a high-statistics dataset obtained using the CLAS at Jefferson Lab for center-of-mass energies from threshold up to 2.4 GeV. This analysis benefits from access to the world's first high-precision spin-density matrix element measurements, available to the event-based PWA through the decay distribution of ω→π+π-π0. The data confirm the dominance of the t-channel π0 exchange amplitude in the forward direction. The dominant resonance contributions are consistent with the previously identified states F15(1680) and D13(1700) near threshold, as well as the G17(2190) at higher energies. Suggestive evidence for the presence of a JP=5/2+ state around 2 GeV, a "missing" state, has also been found. Evidence for other states is inconclusive.