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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	23	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
322.4.a.a	$322$	$4$	322.a	1.a	$1$	$2$	$2$	$18.999$	\(\Q(\sqrt{2}) \)	None	✓	✓			322.4.a.a	$1$	$0$	\(-4\)	\(-4\)	\(16\)	\(14\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(-2+3\beta )q^{3}+4q^{4}+(8-3\beta )q^{5}+\cdots\)
322.4.a.b	$322$	$4$	322.a	1.a	$1$	$2$	$2$	$18.999$	\(\Q(\sqrt{73}) \)	None	✓	✓			322.4.a.b	$1$	$0$	\(-4\)	\(9\)	\(-8\)	\(14\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(5-\beta )q^{3}+4q^{4}+(-2-4\beta )q^{5}+\cdots\)

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