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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	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
56.6.a.a	$56$	$6$	56.a	1.a	$1$	$1$	$1$	$8.981$	\(\Q\)	None	✓	✓	✓	✓	56.6.a.a	$1$	$1$	\(0\)	\(-6\)	\(4\)	\(49\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-6q^{3}+4q^{5}+7^{2}q^{7}-207q^{9}-240q^{11}+\cdots\)
56.6.a.d	$56$	$6$	56.a	1.a	$1$	$2$	$2$	$8.981$	\(\Q(\sqrt{193}) \)	None	✓	✓	✓	✓	56.6.a.d	$1$	$1$	\(0\)	\(-14\)	\(42\)	\(-98\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-7-\beta )q^{3}+(21+5\beta )q^{5}-7^{2}q^{7}+\cdots\)

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