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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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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.d	$196$	$8$	196.a	1.a	$1$	$5$	$5$	$61.227$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				28.8.e.a	$1$	$1$	\(0\)	\(-27\)	\(-249\)	\(0\)		$-$	$+$	$-$	$2^{9}\cdot 3^{2}\cdot 7^{3}$	$\mathrm{SU}(2)$	\(q+(-5-\beta _{1})q^{3}+(-7^{2}-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
196.8.a.f	$196$	$8$	196.a	1.a	$1$	$6$	$6$	$61.227$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓	✓		196.8.a.f	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{4}\cdot 7^{4}$	$\mathrm{SU}(2)$	\(q+(\beta _{1}-\beta _{3})q^{3}+(\beta _{2}+\beta _{3})q^{5}+(50+2\beta _{4}+\cdots)q^{9}+\cdots\)

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