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The results below are complete, since the LMFDB contains all newforms with trivial character and $Nk^2$ at most 40000

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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	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
196.8.a.a	$196$	$8$	196.a	1.a	$1$	$2$	$2$	$61.227$	\(\Q(\sqrt{1009}) \)	None	✓				28.8.a.b	$1$	$0$	\(0\)	\(-14\)	\(294\)	\(0\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-7-\beta )q^{3}+(147+11\beta )q^{5}+(-1129+\cdots)q^{9}+\cdots\)
196.8.a.b	$196$	$8$	196.a	1.a	$1$	$2$	$2$	$61.227$	\(\Q(\sqrt{3529}) \)	None	✓				28.8.a.a	$1$	$0$	\(0\)	\(14\)	\(-42\)	\(0\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(7-\beta )q^{3}+(-21-3\beta )q^{5}+(1391+\cdots)q^{9}+\cdots\)
196.8.a.c	$196$	$8$	196.a	1.a	$1$	$4$	$4$	$61.227$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	✓			196.8.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$2^{7}\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(1769-\beta _{3})q^{9}+\cdots\)
196.8.a.e	$196$	$8$	196.a	1.a	$1$	$5$	$5$	$61.227$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓		✓		28.8.e.a	$1$	$0$	\(0\)	\(27\)	\(249\)	\(0\)		$-$	$-$	$+$	$2^{9}\cdot 3^{2}\cdot 7^{3}$	$\mathrm{SU}(2)$	\(q+(5+\beta _{1})q^{3}+(7^{2}+\beta _{1}-\beta _{2})q^{5}+(1140+\cdots)q^{9}+\cdots\)

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