Studies of auroral energy input at high latitudes often depend on observations of emissions from the first negative band of ionised nitrogen. However, these emissions are affected by solar resonance scattering, which makes photometric and spectrographic measurements difficult to interpret. This work is a statistical study from Longyearbyen, Svalbard, Norway, during the solar minimum between January and March 2007, providing a good coverage in shadow height position and precipitation conditions. The High Throughput Imaging Echelle Spectrograph (HiTIES) measured three bands of N₂⁺ 1N (0,1), (1,2) and (2,3), and one N₂ 2P band (0,3) in the magnetic zenith. The brightness ratios of the N₂⁺ bands are compared with a theoretical treatment with excellent results. Balance equations for all important vibrational levels of the three lowest electronic states of the N₂⁺ molecule are solved for steady-state, and the results combined with ion chemistry modelling. Brightnesses of the (0,1), (1,2) and (2,3) bands of N₂⁺ 1N are calculated for a range of auroral electron energies, and different values of shadow heights. It is shown that in sunlit aurora, the brightness of the (0,1) band is enhanced, with the scattered contribution increasing with decreasing energy of precipitation (10-fold enhancements for energies of 100 eV). The higher vibrational bands are enhanced even more significantly. In sunlit aurora the observed 1N (1,2)/(0,1) and (2,3)/(0,1) ratios increase as a function of decreasing precipitation energy, as predicted by theory. In non-sunlit aurora the N₂⁺ species have a constant proportionality to neutral N₂. The ratio of 2P(0,3)/1N(0,1) in the morning hours shows a pronounced decrease, indicating enhancement of N₂⁺ 1N emission. Finally we study the relationship of all emissions and their ratios to rotational temperatures. A clear effect is observed on rotational development of the bands. It is possible that greatly enhanced rotational temperatures may be a signature of ion upflows.