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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	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
546.8.a.c	$546$	$8$	546.a	1.a	$1$	$1$	$1$	$170.562$	\(\Q\)	None	✓	$1$	$1$	\(8\)	\(27\)	\(-10\)	\(-343\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+8q^{2}+3^{3}q^{3}+2^{6}q^{4}-10q^{5}+6^{3}q^{6}+\cdots\)
546.8.a.e	$546$	$8$	546.a	1.a	$1$	$3$	$3$	$170.562$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(24\)	\(81\)	\(-378\)	\(-1029\)		$-$	$-$	$+$	$-$	$-$	$3$	$\mathrm{SU}(2)$	\(q+8q^{2}+3^{3}q^{3}+2^{6}q^{4}+(-126+\beta _{2})q^{5}+\cdots\)

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