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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 (7 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	5	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
240.4.a.a	$240$	$4$	240.a	1.a	$1$	$1$	$1$	$14.160$	\(\Q\)	None	✓		✓	✓	120.4.a.e	$1$	$0$	\(0\)	\(-3\)	\(-5\)	\(-20\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-5q^{5}-20q^{7}+9q^{9}-2^{4}q^{11}+\cdots\)
240.4.a.c	$240$	$4$	240.a	1.a	$1$	$1$	$1$	$14.160$	\(\Q\)	None	✓				30.4.a.a	$1$	$0$	\(0\)	\(-3\)	\(5\)	\(-32\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+5q^{5}-2^{5}q^{7}+9q^{9}+60q^{11}+\cdots\)
240.4.a.e	$240$	$4$	240.a	1.a	$1$	$1$	$1$	$14.160$	\(\Q\)	None	✓				15.4.a.a	$1$	$0$	\(0\)	\(-3\)	\(5\)	\(24\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+5q^{5}+24q^{7}+9q^{9}-52q^{11}+\cdots\)
240.4.a.f	$240$	$4$	240.a	1.a	$1$	$1$	$1$	$14.160$	\(\Q\)	None	✓				15.4.a.b	$1$	$0$	\(0\)	\(3\)	\(-5\)	\(-20\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-5q^{5}-20q^{7}+9q^{9}+24q^{11}+\cdots\)
240.4.a.i	$240$	$4$	240.a	1.a	$1$	$1$	$1$	$14.160$	\(\Q\)	None	✓				60.4.a.a	$1$	$0$	\(0\)	\(3\)	\(-5\)	\(28\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-5q^{5}+28q^{7}+9q^{9}+24q^{11}+\cdots\)
240.4.a.k	$240$	$4$	240.a	1.a	$1$	$1$	$1$	$14.160$	\(\Q\)	None	✓				120.4.a.d	$1$	$0$	\(0\)	\(3\)	\(5\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+5q^{5}+9q^{9}-4q^{11}+54q^{13}+\cdots\)
240.4.a.l	$240$	$4$	240.a	1.a	$1$	$1$	$1$	$14.160$	\(\Q\)	None	✓				120.4.a.c	$1$	$0$	\(0\)	\(3\)	\(5\)	\(16\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+5q^{5}+2^{4}q^{7}+9q^{9}+28q^{11}+\cdots\)

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