  We discuss a minimal flavour model with twin modular symmetries, leading to
trimaximal 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
$\tau_{SU}$ with residual $Z^{SU}_2$ symmetry, and one acting in the charged
lepton sector, associated with a modulus field value $\tau_{T}$ with residual
$Z^{T}_3$ symmetry. Apart from the predictions of 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.
