Post-accelerated isomerically purified radioactive beams, available at the CERN On-Line Isotope Mass Separator facility using the resonant ionization laser technique, have been used to study the Coulomb excitation of the I π = 3 − state in 70 Cu (Z = 29, N = 41). While first results using a I π = 6 − beam were reported previously, the present complementary experiment allows us to complete the study of the multiplet of states (3 − , 4 − , 5 − , 6 − ) arising from the π 2p 3/2 ν1g 9/2 configuration. Besides the known γ -ray transition deexciting the 4 − state, a ground-state γ ray of 511(3) keV was observed for the first time and was unambiguously associated with the 5 − state deexcitation. This observation fixes the energy, spin, and parity of this state, completing the low-energy level scheme of 70 Cu. B(E2) values for all possible E2 transitions within the multiplet were determined. A comparison with large-scale shell model calculations using different interactions and valence spaces shows the importance of proton excitation across the Z = 28 shell gap and the role of the 2d 5/2 neutron orbital.