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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	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
196.4.a.a	$196$	$4$	196.a	1.a	$1$	$1$	$1$	$11.564$	\(\Q\)	None	✓	✓			196.4.a.a	$1$	$0$	\(0\)	\(-4\)	\(-20\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{3}-20q^{5}-11q^{9}+44q^{11}+\cdots\)
196.4.a.b	$196$	$4$	196.a	1.a	$1$	$1$	$1$	$11.564$	\(\Q\)	None	✓				28.4.a.b	$1$	$0$	\(0\)	\(-4\)	\(-6\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{3}-6q^{5}-11q^{9}-12q^{11}+82q^{13}+\cdots\)
196.4.a.c	$196$	$4$	196.a	1.a	$1$	$1$	$1$	$11.564$	\(\Q\)	None	✓	✓			196.4.a.a	$1$	$0$	\(0\)	\(4\)	\(20\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{3}+20q^{5}-11q^{9}+44q^{11}+\cdots\)
196.4.a.d	$196$	$4$	196.a	1.a	$1$	$1$	$1$	$11.564$	\(\Q\)	None	✓				28.4.a.a	$1$	$0$	\(0\)	\(10\)	\(8\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+10q^{3}+8q^{5}+73q^{9}-40q^{11}+\cdots\)
196.4.a.g	$196$	$4$	196.a	1.a	$1$	$2$	$2$	$11.564$	\(\Q(\sqrt{37}) \)	None	✓		✓		28.4.e.a	$1$	$0$	\(0\)	\(0\)	\(14\)	\(0\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(7+2\beta )q^{5}+10q^{9}+(2^{4}-7\beta )q^{11}+\cdots\)

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