Modular Weights, U(1)'s and Mass Matrices

We derive the scalar mass matrices in effective supergravity models augmented by a $U(1)_F$ family symmetry. Simple relations between $U(1)_F$ charges and modular weights of the superfields are derived and used to express the matrices with a minimum number of parameters. The model predicts a branching ratio for the $\mu\to e\gamma$ process close to the present experimental limits.