# Much ado about 248

## TL;DR

This paper explores three different representations of a 248-dimensional Lie algebra, each associated with trivial ordinary differential equations of varying orders, highlighting the algebra's symmetry properties.

## Contribution

It introduces three novel representations of the 248-dimensional Lie algebra through symmetry analysis of trivial ODE systems of different orders.

## Key findings

- Identifies three distinct Lie algebra representations linked to trivial ODE systems.
- Demonstrates the algebra's symmetry structure across different differential equation orders.
- Provides insights into the algebraic structure underlying trivial ODE systems.

## Abstract

In this note we present three representations of a 248-dimensional Lie algebra, namely the algebra of Lie point symmetries admitted by a system of five trivial ordinary differential equations each of order forty-four, that admitted by a system of seven trivial ordinary differential equations each of order twenty-eight and that admitted by one trivial ordinary differential equation of order two hundred and forty-four.