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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 (9 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.a	$315$	$10$	315.a	1.a	$1$	$1$	$1$	$162.236$	\(\Q\)	None	✓				35.10.a.a	$1$	$1$	\(-28\)	\(0\)	\(-625\)	\(2401\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-28q^{2}+272q^{4}-5^{4}q^{5}+7^{4}q^{7}+\cdots\)
315.10.a.b	$315$	$10$	315.a	1.a	$1$	$2$	$2$	$162.236$	\(\Q(\sqrt{2}) \)	None	✓				35.10.a.b	$1$	$1$	\(24\)	\(0\)	\(-1250\)	\(4802\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(12+\beta )q^{2}+(-360+24\beta )q^{4}-5^{4}q^{5}+\cdots\)
315.10.a.c	$315$	$10$	315.a	1.a	$1$	$4$	$4$	$162.236$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				105.10.a.f	$1$	$1$	\(-8\)	\(0\)	\(2500\)	\(-9604\)		$-$	$-$	$+$	$+$	$2^{6}\cdot 3^{2}\cdot 5$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1})q^{2}+(106-\beta _{1}+\beta _{3})q^{4}+\cdots\)
315.10.a.d	$315$	$10$	315.a	1.a	$1$	$4$	$4$	$162.236$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				105.10.a.e	$1$	$1$	\(-5\)	\(0\)	\(2500\)	\(-9604\)		$-$	$-$	$+$	$+$	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{2}+(237+3\beta _{1}+\beta _{3})q^{4}+\cdots\)
315.10.a.g	$315$	$10$	315.a	1.a	$1$	$4$	$4$	$162.236$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				35.10.a.c	$1$	$1$	\(19\)	\(0\)	\(2500\)	\(-9604\)		$-$	$-$	$+$	$+$	$2\cdot 3^{2}\cdot 5$	$\mathrm{SU}(2)$	\(q+(5+\beta _{1})q^{2}+(435+9\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
315.10.a.i	$315$	$10$	315.a	1.a	$1$	$4$	$4$	$162.236$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				105.10.a.a	$1$	$1$	\(41\)	\(0\)	\(-2500\)	\(9604\)		$-$	$+$	$-$	$+$	$2^{2}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q+(10-\beta _{1})q^{2}+(120-21\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
315.10.a.k	$315$	$10$	315.a	1.a	$1$	$6$	$6$	$162.236$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓		✓		105.10.a.h	$1$	$1$	\(-26\)	\(0\)	\(-3750\)	\(14406\)		$-$	$+$	$-$	$+$	$2^{7}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q+(-4-\beta _{1})q^{2}+(426+3\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
315.10.a.n	$315$	$10$	315.a	1.a	$1$	$8$	$8$	$162.236$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓	✓	✓	315.10.a.n	$1$	$1$	\(-25\)	\(0\)	\(5000\)	\(19208\)		$+$	$-$	$-$	$+$	$2^{10}\cdot 3^{4}$	$\mathrm{SU}(2)$	\(q+(-3-\beta _{1})q^{2}+(233+5\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
315.10.a.p	$315$	$10$	315.a	1.a	$1$	$10$	$10$	$162.236$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓	✓	✓	315.10.a.p	$1$	$1$	\(-7\)	\(0\)	\(-6250\)	\(-24010\)		$+$	$+$	$+$	$+$	$2^{11}\cdot 3^{12}\cdot 5^{4}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(223-\beta _{1}+\beta _{2})q^{4}+\cdots\)

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