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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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Results (4 matches)

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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	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
162.4.a.a	$162$	$4$	162.a	1.a	$1$	$1$	$1$	$9.558$	\(\Q\)	None	✓				18.4.c.a	$1$	$1$	\(-2\)	\(0\)	\(9\)	\(-31\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+4q^{4}+9q^{5}-31q^{7}-8q^{8}+\cdots\)
162.4.a.c	$162$	$4$	162.a	1.a	$1$	$1$	$1$	$9.558$	\(\Q\)	None	✓	✓			162.4.a.b	$1$	$1$	\(2\)	\(0\)	\(-21\)	\(8\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+4q^{4}-21q^{5}+8q^{7}+8q^{8}+\cdots\)
162.4.a.d	$162$	$4$	162.a	1.a	$1$	$1$	$1$	$9.558$	\(\Q\)	None	✓				18.4.c.a	$1$	$1$	\(2\)	\(0\)	\(-9\)	\(-31\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+4q^{4}-9q^{5}-31q^{7}+8q^{8}+\cdots\)
162.4.a.e	$162$	$4$	162.a	1.a	$1$	$2$	$2$	$9.558$	\(\Q(\sqrt{3}) \)	None	✓	✓	✓		162.4.a.e	$1$	$1$	\(-4\)	\(0\)	\(-12\)	\(16\)		$+$	$-$	$-$	$3$	$\mathrm{SU}(2)$	\(q-2q^{2}+4q^{4}+(-6+\beta )q^{5}+(8-2\beta )q^{7}+\cdots\)

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