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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad \(p\)	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
456.2.a.b	$456$	$2$	456.a	1.a	$1$	$1$	$1$	$3.641$	\(\Q\)	None	✓	✓			456.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
456.2.a.e	$456$	$2$	456.a	1.a	$1$	$2$	$2$	$3.641$	\(\Q(\sqrt{41}) \)	None	✓	✓	✓		456.2.a.e	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(-3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta q^{5}+(-2+\beta )q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)

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