  We analyze a modular invariant model of lepton masses, with neutrino masses
originating either from the Weinberg operator or from the seesaw. The
constraint provided by modular invariance is so strong that neutrino mass
ratios, lepton mixing angles and Dirac/Majorana phases do not depend on any
Lagrangian parameter. They only depend on the vacuum of the theory,
parametrized in terms of a complex modulus and a real field. Thus eight
measurable quantities are described by the three vacuum parameters, whose
optimization provides an excellent fit to data for the Weinberg operator and a
good fit for the seesaw case. Neutrino masses from the Weinberg operator
(seesaw) have inverted (normal) ordering. Several sources of potential
corrections, such as higher dimensional operators, renormalization group
evolution and supersymmetry breaking effects, are carefully discussed and shown
not to affect the predictions under reasonable conditions.
