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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	23	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
736.4.a.f	$736$	$4$	736.a	1.a	$1$	$8$	$8$	$43.425$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓			736.4.a.e	$1$	$0$	\(0\)	\(12\)	\(-12\)	\(-14\)		$+$	$+$	$+$	$2^{8}$	$\mathrm{SU}(2)$	\(q+(2-\beta _{1})q^{3}+(-1-\beta _{3})q^{5}+(-2+\cdots)q^{7}+\cdots\)
736.4.a.g	$736$	$4$	736.a	1.a	$1$	$9$	$9$	$43.425$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓	✓		736.4.a.g	$1$	$0$	\(0\)	\(-14\)	\(30\)	\(28\)		$+$	$+$	$+$	$2^{10}$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1})q^{3}+(3-\beta _{4})q^{5}+(3-\beta _{6}+\cdots)q^{7}+\cdots\)

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