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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
1023.1.dk.a	$1023$	$1$	1023.dk	1023.ck	$30$	$8$	$1$	$0.511$	\(\Q(\zeta_{15})\)	$D_{30}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(-3\)	\(0\)	$1$		\(q-\zeta_{30}^{14}q^{3}+\zeta_{30}^{3}q^{4}+(-\zeta_{30}^{9}+\cdots)q^{5}+\cdots\)
1023.1.dk.b	$1023$	$1$	1023.dk	1023.ck	$30$	$8$	$1$	$0.511$	\(\Q(\zeta_{15})\)	$D_{30}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(1\)	\(3\)	\(0\)	$1$		\(q+\zeta_{30}^{8}q^{3}+\zeta_{30}^{3}q^{4}+(\zeta_{30}^{9}-\zeta_{30}^{11}+\cdots)q^{5}+\cdots\)

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