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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
3.72.a.a	$3$	$72$	3.a	1.a	$1$	$5$	$5$	$95.774$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓	✓	✓	3.72.a.a	$1$	$1$	\(-25051277688\)	\(25\!\cdots\!35\)	\(14\!\cdots\!30\)	\(-12\!\cdots\!52\)		$-$	$-$	$2^{36}\cdot 3^{20}\cdot 5^{4}\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q+(-5010255538-\beta _{1})q^{2}+3^{35}q^{3}+\cdots\)

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