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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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Results (1-50 of 130 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
968.1.f.a	$968$	$1$	968.f	8.d	$2$	$2$	$2$	$0.483$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-2}) $	None	✓	$2$	$0$	$-2$	$-1$	$0$	$0$		$1$		$q-q^{2}+(-1+\beta )q^{3}+q^{4}+(1-\beta )q^{6}+\cdots$
968.1.f.b	$968$	$1$	968.f	8.d	$2$	$2$	$2$	$0.483$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-2}) $	None	✓	$2$	$0$	$2$	$-1$	$0$	$0$		$1$		$q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots$
968.1.h.a	$968$	$1$	968.h	11.b	$2$	$2$	$2$	$0.483$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None		$2$	$0$	$0$	$-2$	$2$	$0$		$1$		$q-q^{3}+q^{5}-\beta q^{7}-q^{15}-\beta q^{17}+\cdots$
968.1.j.a	$968$	$1$	968.j	11.d	$10$	$8$	$2$	$0.483$	8.0.64000000.1	$S_{4}$	None	None		$8$	$0$	$0$	$2$	$-2$	$0$		$1$		$q+(1-\beta _{2}+\beta _{4}-\beta _{6})q^{3}+\beta _{4}q^{5}-\beta _{7}q^{7}+\cdots$
968.1.l.a	$968$	$1$	968.l	88.l	$10$	$4$	$1$	$0.483$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$3$	$0$	$0$		$1$		$q-\zeta_{10}q^{2}+(1-\zeta_{10})q^{3}+\zeta_{10}^{2}q^{4}+\cdots$
968.1.l.b	$968$	$1$	968.l	88.l	$10$	$4$	$1$	$0.483$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$-2$	$0$	$0$		$1$		$q+\zeta_{10}q^{2}+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{3}+\zeta_{10}^{2}q^{4}+\cdots$
968.1.l.c	$968$	$1$	968.l	88.l	$10$	$4$	$1$	$0.483$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$3$	$0$	$0$		$1$		$q+\zeta_{10}q^{2}+(1-\zeta_{10})q^{3}+\zeta_{10}^{2}q^{4}+\cdots$
968.1.x.a	$968$	$1$	968.x	968.x	$22$	$10$	$1$	$0.483$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$		$1$		$q+\zeta_{22}^{8}q^{2}+(-\zeta_{22}^{5}+\zeta_{22}^{6})q^{3}+\cdots$
968.1.z.a	$968$	$1$	968.z	968.z	$110$	$40$	$1$	$0.483$	$\Q(\zeta_{55})$	$D_{55}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$2$	$0$	$0$		$1$		$q-\zeta_{110}^{49}q^{2}+(-\zeta_{110}^{21}-\zeta_{110}^{23}+\cdots)q^{3}+\cdots$
968.2.a.a	$968$	$2$	968.a	1.a	$1$	$1$	$1$	$7.730$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-3q^{5}+2q^{7}+6q^{9}+9q^{15}+\cdots$
968.2.a.b	$968$	$2$	968.a	1.a	$1$	$1$	$1$	$7.730$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-4q^{7}-3q^{9}-3q^{13}-3q^{17}+\cdots$
968.2.a.c	$968$	$2$	968.a	1.a	$1$	$1$	$1$	$7.730$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}+4q^{7}-3q^{9}+3q^{13}+3q^{17}+\cdots$
968.2.a.d	$968$	$2$	968.a	1.a	$1$	$1$	$1$	$7.730$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-4q^{7}-2q^{9}-4q^{13}+\cdots$
968.2.a.e	$968$	$2$	968.a	1.a	$1$	$1$	$1$	$7.730$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+4q^{7}-2q^{9}+4q^{13}+\cdots$
968.2.a.f	$968$	$2$	968.a	1.a	$1$	$2$	$2$	$7.730$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$0$	$-2$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+\beta q^{5}+(-1-\beta )q^{7}+\cdots$
968.2.a.g	$968$	$2$	968.a	1.a	$1$	$2$	$2$	$7.730$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$0$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+\beta q^{5}+(1+\beta )q^{7}+(3+\cdots)q^{9}+\cdots$
968.2.a.h	$968$	$2$	968.a	1.a	$1$	$2$	$2$	$7.730$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-1+\beta )q^{5}-\beta q^{7}+(-2+\cdots)q^{9}+\cdots$
968.2.a.i	$968$	$2$	968.a	1.a	$1$	$2$	$2$	$7.730$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-1+\beta )q^{5}+\beta q^{7}+(-2+\cdots)q^{9}+\cdots$
968.2.a.j	$968$	$2$	968.a	1.a	$1$	$2$	$2$	$7.730$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$3$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(2-\beta )q^{5}+2\beta q^{7}+(1+\beta )q^{9}+\cdots$
968.2.a.k	$968$	$2$	968.a	1.a	$1$	$2$	$2$	$7.730$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$-4$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-2-\beta )q^{5}+(-1-\beta )q^{7}+\cdots$
968.2.a.l	$968$	$2$	968.a	1.a	$1$	$2$	$2$	$7.730$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-2-\beta )q^{5}+(1+\beta )q^{7}+\cdots$
968.2.a.m	$968$	$2$	968.a	1.a	$1$	$4$	$4$	$7.730$	4.4.5225.1	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}+(-1+\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots$
968.2.a.n	$968$	$2$	968.a	1.a	$1$	$4$	$4$	$7.730$	4.4.5225.1	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{3}+(-1+\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots$
968.2.c.a	$968$	$2$	968.c	8.b	$2$	$2$	$2$	$7.730$	$\Q(\sqrt{-2}) $	$_{}$	$\Q(\sqrt{-22}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{2}-2q^{4}-2\beta q^{8}+3q^{9}+2\beta q^{13}+\cdots$
968.2.c.b	$968$	$2$	968.c	8.b	$2$	$4$	$4$	$7.730$	$\Q(\sqrt{3}, \sqrt{-5})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+(-1-\beta _{2})q^{4}+(-1-2\beta _{2}+\cdots)q^{5}+\cdots$
968.2.c.c	$968$	$2$	968.c	8.b	$2$	$8$	$8$	$7.730$	8.0.$\cdots$.10	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(-\beta _{2}+\beta _{3})q^{3}+(1+\beta _{3}+\cdots)q^{4}+\cdots$
968.2.c.d	$968$	$2$	968.c	8.b	$2$	$10$	$10$	$7.730$	10.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}-\beta _{1}q^{3}+(\beta _{2}-\beta _{4}-\beta _{6})q^{4}+\cdots$
968.2.c.e	$968$	$2$	968.c	8.b	$2$	$10$	$10$	$7.730$	10.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}-\beta _{6}q^{3}-\beta _{2}q^{4}+\beta _{7}q^{5}+\cdots$
968.2.c.f	$968$	$2$	968.c	8.b	$2$	$10$	$10$	$7.730$	10.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}-\beta _{6}q^{3}-\beta _{2}q^{4}+\beta _{7}q^{5}+\cdots$
968.2.c.g	$968$	$2$	968.c	8.b	$2$	$16$	$16$	$7.730$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{2}+\beta _{5}q^{3}-\beta _{11}q^{4}-\beta _{7}q^{5}+\cdots$
968.2.c.h	$968$	$2$	968.c	8.b	$2$	$20$	$20$	$7.730$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$10$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{15}q^{2}+\beta _{10}q^{3}-\beta _{4}q^{4}+\beta _{6}q^{5}+\cdots$
968.2.c.i	$968$	$2$	968.c	8.b	$2$	$20$	$20$	$7.730$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-10$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{15}q^{2}+\beta _{10}q^{3}-\beta _{4}q^{4}+\beta _{6}q^{5}+\cdots$
968.2.g.a	$968$	$2$	968.g	88.g	$2$	$8$	$8$	$7.730$	8.0.64000000.1	$_{}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-4$	$0$	$0$		$2^{4}\cdot 11^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}-2q^{4}-\beta _{5}q^{6}-2\beta _{1}q^{8}+\cdots$
968.2.g.b	$968$	$2$	968.g	88.g	$2$	$8$	$8$	$7.730$	$\Q(\zeta_{24})$	$_{}$	None	None		$4$	$0$	$0$	$8$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{24}^{4}q^{2}+(1-\zeta_{24}^{2}+\zeta_{24}^{3}-\zeta_{24}^{6}+\cdots)q^{3}+\cdots$
968.2.g.c	$968$	$2$	968.g	88.g	$2$	$20$	$20$	$7.730$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{12}q^{2}-\beta _{5}q^{3}-\beta _{6}q^{4}-\beta _{9}q^{5}+\cdots$
968.2.g.d	$968$	$2$	968.g	88.g	$2$	$32$	$32$	$7.730$		$_{}$	None	None		$4$	$0$	$0$	$-8$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
968.2.g.e	$968$	$2$	968.g	88.g	$2$	$32$	$32$	$7.730$		$_{}$	None	None		$4$	$0$	$0$	$8$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
968.2.i.a	$968$	$2$	968.i	11.c	$5$	$4$	$1$	$7.730$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$-4$	$-5$	$-4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-2\zeta_{10}-2\zeta_{10}^{3})q^{3}+(-2+\zeta_{10}+\cdots)q^{5}+\cdots$
968.2.i.b	$968$	$2$	968.i	11.c	$5$	$4$	$1$	$7.730$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$-4$	$-5$	$4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-2\zeta_{10}-2\zeta_{10}^{3})q^{3}+(-2+\zeta_{10}+\cdots)q^{5}+\cdots$
968.2.i.c	$968$	$2$	968.i	11.c	$5$	$4$	$1$	$7.730$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$1$	$0$	$-2$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\zeta_{10}-\zeta_{10}^{3})q^{3}+(-1+\zeta_{10}+\cdots)q^{5}+\cdots$
968.2.i.d	$968$	$2$	968.i	11.c	$5$	$4$	$1$	$7.730$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$-2$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-\zeta_{10}-\zeta_{10}^{3})q^{3}+(-1+\zeta_{10}+\cdots)q^{5}+\cdots$
968.2.i.e	$968$	$2$	968.i	11.c	$5$	$4$	$1$	$7.730$	$\Q(\zeta_{10})$	$_{}$	None	None		$4$	$0$	$0$	$-1$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}^{2}q^{3}-\zeta_{10}q^{5}-4\zeta_{10}^{3}q^{7}+\cdots$
968.2.i.f	$968$	$2$	968.i	11.c	$5$	$4$	$1$	$7.730$	$\Q(\zeta_{10})$	$_{}$	None	None		$4$	$0$	$0$	$-1$	$-1$	$4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\zeta_{10}^{2}q^{3}-\zeta_{10}q^{5}+4\zeta_{10}^{3}q^{7}+\cdots$
968.2.i.g	$968$	$2$	968.i	11.c	$5$	$4$	$1$	$7.730$	$\Q(\zeta_{10})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-3$	$-4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-3\zeta_{10}q^{5}-4\zeta_{10}^{3}q^{7}+(3-3\zeta_{10}+\cdots)q^{9}+\cdots$
968.2.i.h	$968$	$2$	968.i	11.c	$5$	$4$	$1$	$7.730$	$\Q(\zeta_{10})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-3$	$4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-3\zeta_{10}q^{5}+4\zeta_{10}^{3}q^{7}+(3-3\zeta_{10}+\cdots)q^{9}+\cdots$
968.2.i.i	$968$	$2$	968.i	11.c	$5$	$4$	$1$	$7.730$	$\Q(\zeta_{10})$	$_{}$	None	None		$4$	$0$	$0$	$3$	$3$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-3\zeta_{10}^{2}q^{3}+3\zeta_{10}q^{5}-2\zeta_{10}^{3}q^{7}+\cdots$
968.2.i.j	$968$	$2$	968.i	11.c	$5$	$4$	$1$	$7.730$	$\Q(\zeta_{10})$	$_{}$	None	None		$4$	$0$	$0$	$3$	$3$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-3\zeta_{10}^{2}q^{3}+3\zeta_{10}q^{5}+2\zeta_{10}^{3}q^{7}+\cdots$
968.2.i.k	$968$	$2$	968.i	11.c	$5$	$4$	$1$	$7.730$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$3$	$3$	$3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+(1+\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
968.2.i.l	$968$	$2$	968.i	11.c	$5$	$4$	$1$	$7.730$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$6$	$5$	$-6$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(2\zeta_{10}-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{3}+(2+\cdots)q^{5}+\cdots$
968.2.i.m	$968$	$2$	968.i	11.c	$5$	$4$	$1$	$7.730$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$6$	$5$	$6$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(2\zeta_{10}-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{3}+(2+\cdots)q^{5}+\cdots$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.