# Neutrino Mass and Mixing with $A_5$ Modular Symmetry

## TL;DR

This paper explores how $A_5$ modular symmetry constrains neutrino masses and lepton mixing, constructing modular forms and analyzing models with and without flavons, using numerical methods.

## Contribution

It provides a comprehensive construction of $A_5$ modular forms and develops all minimal models for neutrino masses and mixing within this symmetry framework.

## Key findings

- Neutrino mass and mixing patterns consistent with experimental data.
- Explicit modular forms of weights 2, 4, 6 for level 5.
- Models with both Weinberg operator and type I seesaw mechanism.

## Abstract

We present a comprehensive analysis of neutrino mass and lepton mixing in theories with $A_5$ modular symmetry. We construct the weight 2, weight 4 and weight 6 modular forms of level 5 in terms of Dedekind eta-functions and Klein forms, and their decomposition into irreducible representation of $A_5$. We construct all the simplest models based on $A_5$ modular symmetry, including scenarios of models with and without flavons in the charged lepton sectors. For each case, the neutrino masses can be generated through either the Weinberg operator or the type I seesaw mechanism. We perform an exhaustive numerical analysis, organising our results in an extensive set of figures and tables.