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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	5	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
30.4.a.a	$30$	$4$	30.a	1.a	$1$	$1$	$1$	$1.770$	\(\Q\)	None	✓	✓	✓	✓	30.4.a.a	$1$	$0$	\(-2\)	\(3\)	\(5\)	\(32\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+3q^{3}+4q^{4}+5q^{5}-6q^{6}+\cdots\)
30.4.a.b	$30$	$4$	30.a	1.a	$1$	$1$	$1$	$1.770$	\(\Q\)	None	✓	✓	✓	✓	30.4.a.b	$1$	$0$	\(2\)	\(3\)	\(-5\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots\)

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