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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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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
3480.1.ct.a	$3480$	$1$	3480.ct	3480.bt	$4$	$4$	$2$	$1.737$	\(\Q(\zeta_{8})\)	$D_{4}$	None	\(\Q(\sqrt{174}) \)		$8$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$		\(q+\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-q^{5}+\cdots\)
3480.1.ct.b	$3480$	$1$	3480.ct	3480.bt	$4$	$4$	$2$	$1.737$	\(\Q(\zeta_{8})\)	$D_{4}$	None	\(\Q(\sqrt{174}) \)		$8$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$		\(q+\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}+q^{5}+\cdots\)

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