A Model for Large theta13 Constructed using the Eigenvectors of the S4 Rotation Matrices

A procedure for using the eigenvectors of the elements of the representations of a discrete group in model building is introduced and is used to construct a model that produces a large reactor mixing angle, sin^2(theta13)=2/3 sin^2(pi/16), in agreement with recent neutrino oscillation observations. The model fully constrains the neutrino mass ratios and predicts normal hierarchy with the light neutrino mass, m1~25 meV. Motivated by the model, a new mixing ansatz is postulated which predicts all the mixing angles within 1sigma errors.