The Galois orbit of a Dirichlet character $\chi$ of modulus $q$ and order $n$ is the set $[\chi]:=\{\sigma(\chi): \sigma\in \Gal(\Q(\zeta_n)/\Q)\}$, where $\sigma(\chi)$ denotes the Dirichlet character of modulus $q$ defined by $k \mapsto \sigma(\chi(k))$. The map $\chi\to \sigma(\chi)$ defines a faithful action of the Galois group $\Gal(\Q(\zeta_n)/\Q)$ on the set of Dirichlet characters of modulus $q$ and order $n$, each of which has $\Q(\zeta_n)$ as its field of values.
Knowl status:
- Review status: reviewed
- Last edited by Andrew Sutherland on 2019-01-12 15:36:30
Referred to by:
History:
(expand/hide all)
- character.dirichlet.5.2.bottom
- character.dirichlet.galois_orbit_index
- character.dirichlet.galois_orbit_label
- cmf.decomposition.new.gamma1
- cmf.inner_twist
- cmf.inner_twist_multiplicity
- cmf.label
- cmf.twist
- cmf.twist_multiplicity
- dq.character.dirichlet.extent
- lmfdb/characters/main.py (line 578)
- lmfdb/characters/main.py (line 591)
- lmfdb/characters/templates/Character.html (line 49)
- 2019-01-12 15:36:30 by Andrew Sutherland (Reviewed)