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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
1239.1.h.a	$1239$	$1$	1239.h	1239.h	$2$	$1$	$1$	$0.618$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-59}) \), \(\Q(\sqrt{-1239}) \)	\(\Q(\sqrt{21}) \)	✓	$4$	$0$	\(0\)	\(-1\)	\(2\)	\(1\)	$1$		\(q-q^{3}-q^{4}+2q^{5}+q^{7}+q^{9}+q^{12}+\cdots\)
1239.1.h.b	$1239$	$1$	1239.h	1239.h	$2$	$1$	$1$	$0.618$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-59}) \), \(\Q(\sqrt{-1239}) \)	\(\Q(\sqrt{21}) \)	✓	$4$	$0$	\(0\)	\(1\)	\(-2\)	\(1\)	$1$		\(q+q^{3}-q^{4}-2q^{5}+q^{7}+q^{9}-q^{12}+\cdots\)

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