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Level	Weight	Analytic conductor	\(Nk^2\)	Dim.

Bad \(p\)	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	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.f	$6840$	$2$	6840.a	1.a	$1$	$1$	$1$	$54.618$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{11}-q^{19}+4q^{23}+q^{25}+\cdots\)
6840.2.a.be	$6840$	$2$	6840.a	1.a	$1$	$3$	$3$	$54.618$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-2\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(-2\beta _{1}-\beta _{2})q^{7}+(1-\beta _{1})q^{11}+\cdots\)

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