Quarks at the modular S 4 cusp

We analyse the possibility of describing quark masses, mixing and CP violation in S_4^' modular flavour models without flavons. We focus on the case where the closeness of the modulus to the point of residual ℤ_3^ST symmetry (the cusp) plays a role in generating quark mass hierarchies and discuss the role modular form normalisations play in such constructions. We find that fitting quark data requires explicit CP breaking, unless a second modulus is introduced.