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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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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	23	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
115.4.a.e	$115$	$4$	115.a	1.a	$1$	$5$	$5$	$6.785$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓	✓	✓	115.4.a.e	$1$	$0$	\(6\)	\(4\)	\(-25\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{3}+\cdots\)
115.4.a.f	$115$	$4$	115.a	1.a	$1$	$8$	$8$	$6.785$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓	✓	✓	115.4.a.f	$1$	$0$	\(6\)	\(0\)	\(40\)	\(11\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+\beta _{6}q^{3}+(5+\beta _{2})q^{4}+\cdots\)

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