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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 (10 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
983.1.b.a	$983$	$1$	983.b	983.b	$2$	$1$	$1$	$0.491$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-983}) \)	None	✓	✓			983.1.b.a	$2$	$0$	\(-1\)	\(-1\)	\(0\)	\(-1\)		$1$		\(q-q^{2}-q^{3}+q^{6}-q^{7}+q^{8}+q^{14}+\cdots\)
983.1.b.b	$983$	$1$	983.b	983.b	$2$	$3$	$3$	$0.491$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-983}) \)	None	✓	✓			983.1.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
983.1.b.c	$983$	$1$	983.b	983.b	$2$	$9$	$9$	$0.491$	\(\Q(\zeta_{54})^+\)	$D_{27}$	\(\Q(\sqrt{-983}) \)	None	✓	✓	✓		983.1.b.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$1$		\(q-\beta _{1}q^{2}+(-\beta _{2}+\beta _{7})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
983.2.a.a	$983$	$2$	983.a	1.a	$1$	$28$	$28$	$7.849$		$_{}$	None	None	✓	✓	✓	✓	983.2.a.a	$1$	$1$	\(-7\)	\(-6\)	\(-7\)	\(-25\)	$+$		$\mathrm{SU}(2)$
983.2.a.b	$983$	$2$	983.a	1.a	$1$	$54$	$54$	$7.849$		$_{}$	None	None	✓	✓	✓	✓	983.2.a.b	$1$	$0$	\(8\)	\(6\)	\(7\)	\(31\)	$-$		$\mathrm{SU}(2)$
983.2.c.a	$983$	$2$	983.c	983.c	$491$	$39690$	$81$	$7.849$		$_{}$	None	None		✓	✓	✓	983.2.c.a	$2$	$0$	\(-489\)	\(-487\)	\(-485\)	\(-489\)			$\mathrm{SU}(2)[C_{491}]$
983.4.a.a	$983$	$4$	983.a	1.a	$1$	$109$	$109$	$57.999$		$_{}$	None	None	✓	✓	✓	✓	983.4.a.a	$1$	$1$	\(-19\)	\(-23\)	\(-50\)	\(-225\)	$-$		$\mathrm{SU}(2)$
983.4.a.b	$983$	$4$	983.a	1.a	$1$	$136$	$136$	$57.999$		$_{}$	None	None	✓	✓	✓	✓	983.4.a.b	$1$	$0$	\(17\)	\(25\)	\(50\)	\(223\)	$+$		$\mathrm{SU}(2)$
983.6.a.a	$983$	$6$	983.a	1.a	$1$	$191$	$191$	$157.657$		$_{}$	None	None	✓	✓	✓	✓	983.6.a.a	$1$	$1$	\(-37\)	\(-74\)	\(-247\)	\(-1569\)	$+$		$\mathrm{SU}(2)$
983.6.a.b	$983$	$6$	983.a	1.a	$1$	$218$	$218$	$157.657$		$_{}$	None	None	✓	✓	✓	✓	983.6.a.b	$1$	$0$	\(35\)	\(70\)	\(253\)	\(1567\)	$-$		$\mathrm{SU}(2)$

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