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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 (5 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.b	$240$	$4$	240.a	1.a	$1$	$1$	$1$	$14.160$	\(\Q\)	None	✓		✓	✓	30.4.a.b	$1$	$1$	\(0\)	\(-3\)	\(-5\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-5q^{5}+4q^{7}+9q^{9}+48q^{11}+\cdots\)
240.4.a.d	$240$	$4$	240.a	1.a	$1$	$1$	$1$	$14.160$	\(\Q\)	None	✓		✓	✓	120.4.a.f	$1$	$1$	\(0\)	\(-3\)	\(5\)	\(-8\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+5q^{5}-8q^{7}+9q^{9}-20q^{11}+\cdots\)
240.4.a.g	$240$	$4$	240.a	1.a	$1$	$1$	$1$	$14.160$	\(\Q\)	None	✓				120.4.a.b	$1$	$1$	\(0\)	\(3\)	\(-5\)	\(-20\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-5q^{5}-20q^{7}+9q^{9}+56q^{11}+\cdots\)
240.4.a.h	$240$	$4$	240.a	1.a	$1$	$1$	$1$	$14.160$	\(\Q\)	None	✓				120.4.a.a	$1$	$1$	\(0\)	\(3\)	\(-5\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-5q^{5}-4q^{7}+9q^{9}-72q^{11}+\cdots\)
240.4.a.j	$240$	$4$	240.a	1.a	$1$	$1$	$1$	$14.160$	\(\Q\)	None	✓		✓	✓	60.4.a.b	$1$	$1$	\(0\)	\(3\)	\(5\)	\(-32\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+5q^{5}-2^{5}q^{7}+9q^{9}-6^{2}q^{11}+\cdots\)

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