Associated to each newform $f$ and primitive Dirichlet character $\psi$, there is a unique newform $g:=f\otimes\psi$, the twist of $f$ by $\psi$, that satisfies \[ a_n(g)=\psi(n)a_n(f) \] for all integers $n\ge 1$ coprime to $N$ and the conductor of $\psi$. The newforms $f$ and $g$ are then twist equivalent. When $g$ is a Galois conjugate of $f$, it is said to be an inner twist.
The newform orbit $[g]$ is a twist of the newform orbit $[f]$ by the character orbit $[\psi]$ if some $g\in [g]$ is a twist of $f$ by some $\psi$ in $[\psi]$. This may occur with multiplicity.
Twist equivalence is an equivalence relation. The twist class of a newform or newform orbit is its equivalence class under this relation.
In the LMFDB each twist class is identified by the label of its minimal twist.
- Review status: reviewed
- Last edited by Andrew Sutherland on 2020-02-06 08:03:53
- cmf.minimal_twist
- cmf.twist_minimal
- cmf.twist_multiplicity
- rcs.cande.cmf
- lmfdb/classical_modular_forms/templates/cmf_embedded_newform.html (line 211)
- lmfdb/classical_modular_forms/templates/cmf_newform.html (line 217)
- lmfdb/classical_modular_forms/web_newform.py (line 1043)
- lmfdb/classical_modular_forms/web_newform.py (line 1049)
- lmfdb/classical_modular_forms/web_newform.py (lines 1065-1066)
- lmfdb/classical_modular_forms/web_newform.py (lines 1115-1120)
- lmfdb/classical_modular_forms/web_newform.py (lines 1136-1137)
- 2020-02-06 08:03:53 by Andrew Sutherland (Reviewed)
- 2020-01-03 05:50:44 by Andrew Sutherland
- 2020-01-02 21:30:49 by Andrew Sutherland
- 2020-01-02 21:28:01 by Andrew Sutherland