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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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Results (3 matches)

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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	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
441.6.a.e	$441$	$6$	441.a	1.a	$1$	$1$	$1$	$70.729$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓				63.6.e.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2^{5}q^{4}-427q^{13}+2^{10}q^{16}+3143q^{19}+\cdots\)
441.6.a.bc	$441$	$6$	441.a	1.a	$1$	$6$	$6$	$70.729$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓				63.6.e.f	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(30+\beta _{3})q^{4}+(-2\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
441.6.a.be	$441$	$6$	441.a	1.a	$1$	$8$	$8$	$70.729$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓	✓		441.6.a.be	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$2^{5}\cdot 7^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{4}q^{2}+(3-\beta _{2})q^{4}+\beta _{1}q^{5}+(-\beta _{4}+\cdots)q^{8}+\cdots\)

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