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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	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
672.4.a.m	$672$	$4$	672.a	1.a	$1$	$2$	$2$	$39.649$	\(\Q(\sqrt{137}) \)	None	✓	$1$	$0$	\(0\)	\(6\)	\(10\)	\(14\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+3q^{3}+(5-\beta )q^{5}+7q^{7}+9q^{9}+(11+\cdots)q^{11}+\cdots\)
672.4.a.r	$672$	$4$	672.a	1.a	$1$	$3$	$3$	$39.649$	3.3.37341.1	None	✓	$1$	$0$	\(0\)	\(9\)	\(6\)	\(21\)		$+$	$-$	$-$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q+3q^{3}+(2-\beta _{1})q^{5}+7q^{7}+9q^{9}+\cdots\)

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