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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	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
252.8.a.a	$252$	$8$	252.a	1.a	$1$	$1$	$1$	$78.721$	\(\Q\)	None	✓				84.8.a.a	$1$	$0$	\(0\)	\(0\)	\(-100\)	\(-343\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-10^{2}q^{5}-7^{3}q^{7}-2774q^{11}-3294q^{13}+\cdots\)
252.8.a.d	$252$	$8$	252.a	1.a	$1$	$2$	$2$	$78.721$	\(\Q(\sqrt{21961}) \)	None	✓				84.8.a.d	$1$	$0$	\(0\)	\(0\)	\(-96\)	\(-686\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-48-\beta )q^{5}-7^{3}q^{7}+(-2070+\cdots)q^{11}+\cdots\)
252.8.a.f	$252$	$8$	252.a	1.a	$1$	$2$	$2$	$78.721$	\(\Q(\sqrt{1009}) \)	None	✓				28.8.a.b	$1$	$0$	\(0\)	\(0\)	\(294\)	\(-686\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(147-11\beta )q^{5}-7^{3}q^{7}+(1746+182\beta )q^{11}+\cdots\)

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