Background: Discrepancies exist between the observed abundances of argon and calcium in oxygen-neon nova ejecta and those predicted by nova models. An improved characterization of the 38K(p ,γ )39Ca reaction rate over the nova temperature regime (∼0.1 -0.4 GK), and thus the nuclear structure of 39Ca above the proton threshold [5770.92(63) keV], is necessary to resolve these contradictions.Purpose: The present study was performed to search for low-spin proton resonances in the 38K+p system, and to improve the uncertainties in energies of the known astrophysically significant proton resonances in 39Ca. Methods: The level structure of 39Ca was investigated via high-resolution charged-particle spectroscopy with an Enge split-pole spectrograph using the 40Ca(3He,α )39Ca reaction. Differential cross sections were measured over six laboratory angles at 21 MeV. Distorted-wave Born approximation calculations were performed to constrain the spin-parity assignments of observed levels with special attention to those significant in determination of the 38K(p ,γ )39Ca reaction rate over the nova temperature regime. Results: The resonance energies corresponding to two out of three astrophysically important states at 6154(5) and 6472.2(24) keV are measured with better precision than previous charged-particle spectroscopy measurements. A tentatively new state is discovered at 5908(3) keV. The spin-parity assignments of a few of the astrophysically important resonances are determined. Conclusions: The present 38K(p ,γ )39Ca upper limit thermonuclear reaction rate at 0.1-0.4 GK is higher than that determined by Christian et al. [Phys. Rev. C 97, 025802 (2018), 10.1103/PhysRevC.97.025802] by at most a factor of 1.4 at 0.1 GK.