Minimal Modular Flavor Symmetry and Lepton Textures Near Fixed Points

An extension of the Standard Model with $Γ_2\simeq S_3$ modular flavor symmetry is presented. We consider the construction of the lepton sector, augmented by two right-handed neutrino states, in the vicinity of the fixed points $τ= i\infty $, $τ= i$ and $τ\!=\!ω\!=\!-\frac{1}{2}\!+\!i\frac{\sqrt{3}}