# Overview

An *Artin representation* is a complex representation of ${\operatorname{Gal}}(\bar{\mathbb{Q}}/{\mathbb{Q}})$ that factors through some finite quotient ${\operatorname{Gal}}(F/{\mathbb{Q}})$. In Magma, Artin representations are represented as characters of ${\operatorname{Gal}}(F/{\mathbb{Q}})$, not the actual modules. They are allowed to be virtual, except in the $L$-function machinery (see Chapter [$L$-series](../../ModularArithmeticGeometry/ModularAbelianVarieties/lser.md#lser)).