Trimaximal TM1 mixing with two modular S4 groups

We discuss a minimal flavor model with twin modular symmetries, leading to trimaximal ${\mathrm{TM}}_{1}$ 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 ${\ensuremath{\tau}}_{SU}$ with residual ${Z}_{2}^{SU}$ symmetry, and one acting in the charged lepton sector, associated with a modulus field value ${\ensuremath{\tau}}_{T}$ with residual ${Z}_{3}^{T}$ symmetry. Apart from the predictions of ${\mathrm{TM}}_{1}$ 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.