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In a class of neutrino mass models with modular flavor symmetries, it hasbeen observed that CP symmetry is preserved at the fixed point (or stabilizer)of the modulus parameter $\tau = {\rm i}$, whereas significant CP violationemerges within the neighbourhood of this stabilizer. In this paper, we firstconstruct a viable model with the modular $A^\prime_5$ symmetry, and explorethe phenomenological implications for lepton masses and flavor mixing. Then, weintroduce explicit perturbations to the stabilizer at $\tau = {\rm i}$, andpresent both numerical and analytical results to understand why a smalldeviation from the stabilizer leads to large CP violation. As low-energyobservables are very sensitive to the perturbations to model parameters, wefurther demonstrate that the renormalization-group running effects play animportant role in confronting theoretical predictions at the high-energy scalewith experimental measurements at the low-energy scale.

Explicit Perturbations to the Stabilizer $\tau = {\rm i}$ of Modular $A^\prime_5$ Symmetry and Leptonic CP Violation