↑

Learn more

Refine search

Level	Weight	Analytic conductor	\(Nk^2\)	Dim.

Bad \(p\)	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
		Only for weight 1:

				Sort order	Select

Results (displaying both matches)

Download displayed columns for results to

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
1291.1.b.a	$1291$	$1$	1291.b	1291.b	$2$	$1$	$1$	$0.644$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1291}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)	$1$		\(q+q^{4}-q^{5}+2q^{7}+q^{9}-q^{13}+q^{16}+\cdots\)
1291.1.b.b	$1291$	$1$	1291.b	1291.b	$2$	$3$	$3$	$0.644$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-1291}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-3\)	$1$		\(q+q^{4}-\beta _{1}q^{5}-q^{7}+q^{9}+\beta _{2}q^{13}+\cdots\)

Download displayed columns for results to