As a result of a new improved fit to old bubble chamber data of the dominant axial C A 5 nucleonto-Delta form factor, and due to the relevance of this form factor for neutrino induced coherent pion production, we re-evaluate our model predictions in Phys. Rev. D 79, 013002 (2009) for different observables of the latter reaction. Central values for the total cross sections increase by 20%∼30%, while differential cross sections do not change their shape appreciably. Furthermore, we also compute the uncertainties on total, differential and flux averaged cross sections induced by the errors in the determination of C A 5 . Our new results turn out to be compatible within about 1σ with the former ones. Finally, we stress the existing tension between the recent experimental determination of the σ(CCcohπ + ) σ(NCcohπ 0 ) ratio by the SciBooNE Collaboration and the theoretical predictions.