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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	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6840.2.a.bp	$6840$	$2$	6840.a	1.a	$1$	$4$	$4$	$54.618$	4.4.20308.1	None	✓	✓	✓	✓	6840.2.a.bp	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-4\)		$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}+(-1+\beta _{1})q^{7}+(1-\beta _{1}-\beta _{3})q^{11}+\cdots\)
6840.2.a.bq	$6840$	$2$	6840.a	1.a	$1$	$4$	$4$	$54.618$	4.4.20308.1	None	✓	✓	✓	✓	6840.2.a.bp	$1$	$1$	\(0\)	\(0\)	\(4\)	\(-4\)		$+$	$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}+(-1+\beta _{1})q^{7}+(-1+\beta _{1}+\beta _{3})q^{11}+\cdots\)

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