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In the framework of the modular symmetry approach to lepton flavour, weconsider a class of theories where matter superfields transform inrepresentations of the finite modular group $\Gamma_5 \simeq A_5$. Weexplicitly construct a basis for the 11 modular forms of weight 2 and level 5.We show how these forms arrange themselves into two triplets and a quintet of$A_5$. We also present multiplets of modular forms of higher weight. Finally,we provide an example of application of our results, constructing two models ofneutrino masses and mixing based on the supersymmetric Weinberg operator.

Modular $A_5$ Symmetry for Flavour Model Building