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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	5	23	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1840.4.a.w	$1840$	$4$	1840.a	1.a	$1$	$8$	$8$	$108.564$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(6\)	\(-40\)	\(3\)		$+$	$+$	$+$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}-5q^{5}-\beta _{5}q^{7}+(8-\beta _{1}+\cdots)q^{9}+\cdots\)
1840.4.a.bb	$1840$	$4$	1840.a	1.a	$1$	$10$	$10$	$108.564$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-50\)	\(-28\)		$+$	$+$	$+$	$+$	$2^{7}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-5q^{5}+(-3-\beta _{1}-\beta _{6})q^{7}+\cdots\)

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