An amplitude analysis of the decay Λb0 → D0pπ− is performed in the part of the phase space containing resonances in the D0p channel. The study is based on a data sample corresponding to an integrated luminosity of 3.0 fb−1 of pp collisions recorded by the LHCb experiment. The spectrum of excited Λc+ states that decay into D0p is studied. The masses, widths and quantum numbers of the Λc(2880)+ and Λc(2940)+ resonances are measured. The constraints on the spin and parity for the Λc(2940)+ state are obtained for the first time. A near-threshold enhancement in the D0p amplitude is investigated and found to be consistent with a new resonance, denoted the Λc(2860)+, of spin 3/2 and positive parity.