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The results below are complete, since the LMFDB contains all newforms with $Nk^2$ at most 4000

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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	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
176.4.a.a	$176$	$4$	176.a	1.a	$1$	$1$	$1$	$10.384$	\(\Q\)	None	✓				88.4.a.b	$1$	$1$	\(0\)	\(-7\)	\(9\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-7q^{3}+9q^{5}-2q^{7}+22q^{9}+11q^{11}+\cdots\)
176.4.a.c	$176$	$4$	176.a	1.a	$1$	$1$	$1$	$10.384$	\(\Q\)	None	✓				22.4.a.c	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(10\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{5}+10q^{7}-26q^{9}-11q^{11}+\cdots\)
176.4.a.d	$176$	$4$	176.a	1.a	$1$	$1$	$1$	$10.384$	\(\Q\)	None	✓				88.4.a.a	$1$	$1$	\(0\)	\(1\)	\(-7\)	\(6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-7q^{5}+6q^{7}-26q^{9}+11q^{11}+\cdots\)
176.4.a.f	$176$	$4$	176.a	1.a	$1$	$1$	$1$	$10.384$	\(\Q\)	None	✓				22.4.a.a	$1$	$1$	\(0\)	\(7\)	\(-19\)	\(-14\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+7q^{3}-19q^{5}-14q^{7}+22q^{9}-11q^{11}+\cdots\)
176.4.a.g	$176$	$4$	176.a	1.a	$1$	$2$	$2$	$10.384$	\(\Q(\sqrt{97}) \)	None	✓		✓		44.4.a.b	$1$	$1$	\(0\)	\(-9\)	\(11\)	\(-10\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-4-\beta )q^{3}+(6-\beta )q^{5}+(-8+6\beta )q^{7}+\cdots\)

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