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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 (3 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
2016.1.dp.a	$2016$	$1$	2016.dp	224.v	$8$	$4$	$1$	$1.006$	\(\Q(\zeta_{8})\)	$D_{8}$	\(\Q(\sqrt{-7}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}-\zeta_{8}^{3}q^{8}+\cdots\)
2016.1.dp.b	$2016$	$1$	2016.dp	224.v	$8$	$4$	$1$	$1.006$	\(\Q(\zeta_{8})\)	$D_{8}$	\(\Q(\sqrt{-7}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{7}+\zeta_{8}q^{8}+\cdots\)
2016.1.dp.c	$2016$	$1$	2016.dp	224.v	$8$	$4$	$1$	$1.006$	\(\Q(\zeta_{8})\)	$D_{8}$	\(\Q(\sqrt{-7}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{3}q^{8}+\cdots\)

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