Modular invariance

Pure mathematics

Mathematical physics

Particle physics

Modular group

Dedekind cut

Operating system

Neutrino

Computer science

Statistical physics

Modular design

Modular form

Thermodynamics

Physics

Homogeneous

Mathematics

Invariant (physics)

Combinatorics

Modular curve

Journal of High Energy Physics

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 $\Gamma'_N$ which is the double covering of $\Gamma_N$. The lowest weight 1 modular forms of level 3 are constructed in terms of Dedekind eta-function, and they transform as a doublet of $\Gamma'_3 \cong T'$. 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.

Neutrino masses and mixing from double covering of finite modular groups