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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
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Results (4 matches)

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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
3224.1.n.a	$3224$	$1$	3224.n	3224.n	$2$	$3$	$3$	$1.609$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-806}) \)	None	✓	$2$	$0$	\(-3\)	\(-1\)	\(1\)	\(0\)	$1$		\(q-q^{2}-\beta _{1}q^{3}+q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
3224.1.n.b	$3224$	$1$	3224.n	3224.n	$2$	$3$	$3$	$1.609$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-806}) \)	None	✓	$2$	$0$	\(-3\)	\(1\)	\(1\)	\(0\)	$1$		\(q-q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
3224.1.n.c	$3224$	$1$	3224.n	3224.n	$2$	$3$	$3$	$1.609$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-806}) \)	None	✓	$2$	$0$	\(3\)	\(-1\)	\(-1\)	\(0\)	$1$		\(q+q^{2}-\beta _{1}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
3224.1.n.d	$3224$	$1$	3224.n	3224.n	$2$	$3$	$3$	$1.609$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-806}) \)	None	✓	$2$	$0$	\(3\)	\(1\)	\(-1\)	\(0\)	$1$		\(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots\)

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