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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
392.6.a.k	$392$	$6$	392.a	1.a	$1$	$5$	$5$	$62.870$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				56.6.i.b	$1$	$1$	\(0\)	\(5\)	\(-81\)	\(0\)		$+$	$+$	$+$	$2^{9}\cdot 7$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+(-2^{4}-\beta _{1}-\beta _{2})q^{5}+\cdots\)
392.6.a.m	$392$	$6$	392.a	1.a	$1$	$6$	$6$	$62.870$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓	✓		392.6.a.m	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$2^{4}\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(\beta _{1}-\beta _{3})q^{5}+(-20+\beta _{4}+\cdots)q^{9}+\cdots\)

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