Abstract
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 \( {\Gamma}_N^{\prime } \) which is the double covering of ΓN. The lowest weight 1 modular forms of level 3 are constructed in terms of Dedekind eta-function, and they transform as a doublet of \( {\Gamma}_3^{\prime } \) ≅ 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.
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Liu, XG., Ding, GJ. Neutrino masses and mixing from double covering of finite modular groups. J. High Energ. Phys. 2019, 134 (2019). https://doi.org/10.1007/JHEP08(2019)134
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DOI: https://doi.org/10.1007/JHEP08(2019)134