# Modular $A_5$ Symmetry for Flavour Model Building

## TL;DR

This paper develops a modular symmetry framework using the finite group A_5 for lepton flavor models, explicitly constructing modular forms and applying them to neutrino mass and mixing models.

## Contribution

It explicitly constructs modular forms of weight 2 and level 5 for A_5, and demonstrates their application in neutrino mass and mixing models.

## Key findings

- Constructed 11 modular forms of weight 2, level 5, forming A_5 representations.
- Presented two neutrino mass and mixing models based on these modular forms.
- Provided higher weight modular form multiplets for flavor model building.

## Abstract

In the framework of the modular symmetry approach to lepton flavour, we consider a class of theories where matter superfields transform in representations of the finite modular group $\Gamma_5 \simeq A_5$. We explicitly 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 of neutrino masses and mixing based on the supersymmetric Weinberg operator.