An Artin representation is a continuous homomorphism $\rho:\mathrm{Gal}(\overline{\Q}/\Q)\to\GL(V)$ from the absolute Galois group of $\Q$ to the automorphism group of a finite-dimensional $\C$-vector space $V$. Here continuity means that $\rho$ factors through the Galois group of some finite extension $K/\Q$, called the Artin field.

The database currently contains approximately 94,000 Artin representations, for a total of 35,000 Artin fields. There are no assertions of completeness of the data.

Browse Artin representations

By dimension: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

By conductor: 1-100, 101-1000, 1001-10000, 10001-100000

By group: $D_4$, $Q_8$, $A_4$, $S_4$, $\GL(2,3)$, $A_5$, $C_3^2:D_4$, $S_5$, $\GL(3,2)$, $A_6$, $S_6$, $A_7$, $S_7$

Search for an Artin representation

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Dimension e.g. 1, 2-4
Conductor e.g. 50, 100-200
Group e.g. C5, or 8T12, a list of group labels
Ramified primes e.g. 2, 3 (no range allowed)
Unramified primes e.g. 5, 7, 13 (no range allowed)
Root number at the moment, one of 1 or -1
Frobenius-Schur indicator +1 for orthogonal, -1 for symplectic, 0 for non-real character
Maximum number of Artin representations to display