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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 (4 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
42.8.a.a	$42$	$8$	42.a	1.a	$1$	$1$	$1$	$13.120$	\(\Q\)	None	✓	✓	✓	✓	42.8.a.a	$1$	$0$	\(-8\)	\(-27\)	\(-410\)	\(-343\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}-410q^{5}+\cdots\)
42.8.a.d	$42$	$8$	42.a	1.a	$1$	$1$	$1$	$13.120$	\(\Q\)	None	✓	✓	✓	✓	42.8.a.d	$1$	$0$	\(-8\)	\(27\)	\(270\)	\(343\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-8q^{2}+3^{3}q^{3}+2^{6}q^{4}+270q^{5}+\cdots\)
42.8.a.e	$42$	$8$	42.a	1.a	$1$	$1$	$1$	$13.120$	\(\Q\)	None	✓	✓	✓	✓	42.8.a.e	$1$	$0$	\(8\)	\(-27\)	\(30\)	\(343\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}+30q^{5}-6^{3}q^{6}+\cdots\)
42.8.a.f	$42$	$8$	42.a	1.a	$1$	$1$	$1$	$13.120$	\(\Q\)	None	✓	✓	✓	✓	42.8.a.f	$1$	$0$	\(8\)	\(27\)	\(470\)	\(-343\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+8q^{2}+3^{3}q^{3}+2^{6}q^{4}+470q^{5}+\cdots\)

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