Trimaximal TM1 mixing with two modular S4 groups

We discuss a minimal flavor model with twin modular symmetries, leading to trimaximal TM1 lepton mixing in which the first column of the tri-bimaximal lepton mixing matrix is preserved. The model involves two modular S-4 groups, one acting in the neutrino sector, associated with a modulus field value tau(SU) with residual Z(2)(SU) symmetry, and one acting in the charged lepton sector, associated with a modulus field value tau(T) with residual Z(3)(T) symmetry. Apart from the predictions of TM1 mixing, the model leads to a new neutrino mass sum rule which implies lower bounds on neutrino masses close to current limits from neutrinoless double beta decay experiments and cosmology.