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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		19	211	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4009.2.a.b	$4009$	$2$	4009.a	1.a	$1$	$3$	$3$	$32.012$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(2\)	\(-2\)	\(-3\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(-1+\beta _{1})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots\)
4009.2.a.c	$4009$	$2$	4009.a	1.a	$1$	$71$	$71$	$32.012$		None	✓	$1$	$1$	\(-15\)	\(-8\)	\(-18\)	\(-19\)		$-$	$-$	$+$		$\mathrm{SU}(2)$

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