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).