An exact numerical approach is used to compute the rotational part of the line strengths (Hönl–London factors) for the [Formula: see text], [Formula: see text] transition (1NG bands). The computed Hönl–London factors enable a synthetic spectrum to be derived, which is then fitted as a final step to observed auroral [Formula: see text] 1NG bands by use of a least squares method. In this way we determine the population densities of the vibrational levels of the upper [Formula: see text] electronic state and, in addition, an average rotational temperature. Our results give clear evidence that the auroral [Formula: see text] 1NG bands are mainly generated by particle impact on neutral O2 molecules in their electronic and vibrational ground states, and that the bands are produced within the E region.