Neutrino masses and mixing from double covering of finite modular groups

A bstract We extend the even weight modular forms of modular invariant approach to general integral weight modular forms. We find that the modular forms of integral weights and level N can be arranged into irreducible representations of the homogeneous finite modular group ΓN Γ N ′ which is the double covering of Γ N . The lowest weight 1 modular forms of level 3 are constructed in terms of Dedekind eta-function, and they transform as a doublet of Γ₃ Γ 3 ′ ≅ T′ . The modular forms of weights 2, 3, 4, 5 and 6 are presented. We build a model of lepton masses and mixing based on T′ modular symmetry.