Multiple realizations of modular flavor symmetries and their phenomenology

We point out that specifying the finite modular group does not uniquely fix a modular flavor symmetry. We illustrate this using the finite modular group $T^{\mathrm{\prime }}$. Otherwise equivalent models based on different $T^{\mathrm{\prime }}$ lead to modular forms with different properties and, hence, produce different phenomenological features. We exemplify this in various scenarios, and show that the ability of a given model to accommodate mass and other observed hierarchies depends sensitively on the way the $T^{\mathrm{\prime }}$ is implemented.