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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	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
2.68.a.a	$2$	$68$	2.a	1.a	$1$	$3$	$3$	$56.858$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	✓	✓	2.68.a.a	$1$	$0$	\(-25769803776\)	\(-52\!\cdots\!16\)	\(-26\!\cdots\!50\)	\(21\!\cdots\!12\)		$+$	$+$	$2^{24}\cdot 3^{5}\cdot 5^{3}\cdot 11\cdot 17$	$\mathrm{SU}(2)$	\(q-2^{33}q^{2}+(-1741882068537572+\cdots)q^{3}+\cdots\)
2.68.a.b	$2$	$68$	2.a	1.a	$1$	$3$	$3$	$56.858$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	✓	✓	2.68.a.b	$1$	$1$	\(25769803776\)	\(-23\!\cdots\!44\)	\(69\!\cdots\!90\)	\(-46\!\cdots\!92\)		$-$	$-$	$2^{24}\cdot 3^{7}\cdot 5^{2}\cdot 7\cdot 11$	$\mathrm{SU}(2)$	\(q+2^{33}q^{2}+(-794134480773348+\cdots)q^{3}+\cdots\)

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