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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 (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	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
56.8.a.a	$56$	$8$	56.a	1.a	$1$	$1$	$1$	$17.494$	\(\Q\)	None	✓	✓			56.8.a.a	$1$	$1$	\(0\)	\(-18\)	\(160\)	\(-343\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-18q^{3}+160q^{5}-7^{3}q^{7}-1863q^{9}+\cdots\)
56.8.a.b	$56$	$8$	56.a	1.a	$1$	$1$	$1$	$17.494$	\(\Q\)	None	✓	✓			56.8.a.b	$1$	$1$	\(0\)	\(46\)	\(-160\)	\(-343\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+46q^{3}-160q^{5}-7^{3}q^{7}-71q^{9}+\cdots\)
56.8.a.c	$56$	$8$	56.a	1.a	$1$	$2$	$2$	$17.494$	\(\Q(\sqrt{249}) \)	None	✓	✓	✓	✓	56.8.a.c	$1$	$1$	\(0\)	\(-42\)	\(14\)	\(686\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-21-3\beta )q^{3}+(7+11\beta )q^{5}+7^{3}q^{7}+\cdots\)

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