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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	7	23	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4025.2.a.w	$4025$	$2$	4025.a	1.a	$1$	$8$	$8$	$32.140$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(2\)	\(0\)	\(-8\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(\beta _{6}+\cdots)q^{6}+\cdots\)
4025.2.a.bd	$4025$	$2$	4025.a	1.a	$1$	$21$	$21$	$32.140$		None	✓	$1$	$0$	\(-2\)	\(1\)	\(0\)	\(-21\)		$-$	$+$	$+$	$-$		$\mathrm{SU}(2)$

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