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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	5	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
315.10.a.f	$315$	$10$	315.a	1.a	$1$	$4$	$4$	$162.236$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				105.10.a.c	$1$	$0$	\(17\)	\(0\)	\(-2500\)	\(-9604\)		$-$	$+$	$+$	$-$	$2^{2}\cdot 3^{2}\cdot 5$	$\mathrm{SU}(2)$	\(q+(4+\beta _{1})q^{2}+(235+9\beta _{1}+\beta _{3})q^{4}+\cdots\)
315.10.a.h	$315$	$10$	315.a	1.a	$1$	$4$	$4$	$162.236$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				105.10.a.b	$1$	$0$	\(20\)	\(0\)	\(-2500\)	\(-9604\)		$-$	$+$	$+$	$-$	$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(5-\beta _{1})q^{2}+(106-8\beta _{1}+2\beta _{2})q^{4}+\cdots\)
315.10.a.l	$315$	$10$	315.a	1.a	$1$	$6$	$6$	$162.236$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓		✓		35.10.a.e	$1$	$0$	\(-15\)	\(0\)	\(-3750\)	\(-14406\)		$-$	$+$	$+$	$-$	$2^{3}\cdot 3^{4}\cdot 5$	$\mathrm{SU}(2)$	\(q+(-3+\beta _{1})q^{2}+(503-3\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)

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