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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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
169.10.a.e	$169$	$10$	169.a	1.a	$1$	$10$	$10$	$87.041$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓				13.10.b.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$-$	$-$	$2^{10}\cdot 3^{4}\cdot 13^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(2^{8}+\beta _{2})q^{4}+(-6\beta _{1}+\cdots)q^{5}+\cdots\)
169.10.a.f	$169$	$10$	169.a	1.a	$1$	$20$	$20$	$87.041$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓				13.10.e.a	$2$	$0$	\(0\)	\(326\)	\(0\)	\(0\)		$-$	$-$	$2^{25}\cdot 3^{10}\cdot 13^{12}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2^{4}+\beta _{4})q^{3}+(2^{8}+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
169.10.a.h	$169$	$10$	169.a	1.a	$1$	$27$	$27$	$87.041$		None	✓	✓	✓		169.10.a.g	$1$	$0$	\(65\)	\(1\)	\(3238\)	\(17378\)		$-$	$-$		$\mathrm{SU}(2)$

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