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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
441.4.a.w	$441$	$4$	441.a	1.a	$1$	$4$	$4$	$26.020$	4.4.6257832.1	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(\beta _{1}+\beta _{3})q^{5}+\cdots\)
441.4.a.x	$441$	$4$	441.a	1.a	$1$	$8$	$8$	$26.020$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$2^{4}\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(8-\beta _{3})q^{4}+\beta _{1}q^{5}+(-11\beta _{2}+\cdots)q^{8}+\cdots\)

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