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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 (3 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	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
396.4.a.a	$396$	$4$	396.a	1.a	$1$	$1$	$1$	$23.365$	\(\Q\)	None	✓				132.4.a.c	$1$	$0$	\(0\)	\(0\)	\(-22\)	\(-20\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-22q^{5}-20q^{7}-11q^{11}+22q^{13}+\cdots\)
396.4.a.f	$396$	$4$	396.a	1.a	$1$	$1$	$1$	$23.365$	\(\Q\)	None	✓				132.4.a.a	$1$	$0$	\(0\)	\(0\)	\(12\)	\(14\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+12q^{5}+14q^{7}-11q^{11}+56q^{13}+\cdots\)
396.4.a.i	$396$	$4$	396.a	1.a	$1$	$2$	$2$	$23.365$	\(\Q(\sqrt{97}) \)	None	✓		✓		44.4.a.b	$1$	$0$	\(0\)	\(0\)	\(-11\)	\(10\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-5-\beta )q^{5}+(2+6\beta )q^{7}-11q^{11}+\cdots\)

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