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 94000 Artin representations, for a total of 35000 Artin fields.

## Browse Artin representations

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

## Search for an Artin representation

Please enter a value or leave blank:

 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