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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 (1-50 of 207 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
96.2.a.a	$96$	$2$	96.a	1.a	$1$	$1$	$1$	$0.767$	$\Q$	None	✓	✓	✓	✓	96.2.a.a	$1$	$0$	$0$	$-1$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots$
96.2.a.b	$96$	$2$	96.a	1.a	$1$	$1$	$1$	$0.767$	$\Q$	None	✓	✓	✓	✓	96.2.a.a	$1$	$0$	$0$	$1$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots$
96.2.c.a	$96$	$2$	96.c	12.b	$2$	$4$	$4$	$0.767$	$\Q(\zeta_{8})$	None		✓	✓	✓	96.2.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{8}q^{3}+\zeta_{8}^{3}q^{5}+(-\zeta_{8}+\zeta_{8}^{2})q^{7}+\cdots$
96.2.d.a	$96$	$2$	96.d	8.b	$2$	$2$	$2$	$0.767$	$\Q(\sqrt{-1}) $	None			✓	✓	24.2.d.a	$2$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+2iq^{5}+2q^{7}-q^{9}-4iq^{13}+\cdots$
96.2.f.a	$96$	$2$	96.f	24.f	$2$	$2$	$2$	$0.767$	$\Q(\sqrt{-2}) $	$\Q(\sqrt{-2}) $			✓	✓	24.2.f.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(1+\beta )q^{3}+(-1+2\beta )q^{9}-2\beta q^{11}+\cdots$
96.2.n.a	$96$	$2$	96.n	32.g	$8$	$32$	$8$	$0.767$		None		✓	✓	✓	96.2.n.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
96.2.o.a	$96$	$2$	96.o	96.o	$8$	$56$	$14$	$0.767$		None		✓	✓	✓	96.2.o.a	$4$	$0$	$0$	$-4$	$0$	$-8$			$\mathrm{SU}(2)[C_{8}]$
96.3.b.a	$96$	$3$	96.b	8.d	$2$	$4$	$4$	$2.616$	4.0.4752.1	None			✓	✓	24.3.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}-\beta _{2}q^{5}+(-\beta _{2}-\beta _{3})q^{7}+\cdots$
96.3.e.a	$96$	$3$	96.e	3.b	$2$	$4$	$4$	$2.616$	$\Q(\sqrt{-2}, \sqrt{3})$	None		✓			96.3.e.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{2}q^{5}+(2\beta _{1}-\beta _{3})q^{7}+(-3+\cdots)q^{9}+\cdots$
96.3.e.b	$96$	$3$	96.e	3.b	$2$	$4$	$4$	$2.616$	$\Q(\sqrt{-2}, \sqrt{7})$	None		✓			96.3.e.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{3})q^{3}-\beta _{2}q^{5}+(-\beta _{1}-2\beta _{3})q^{7}+\cdots$
96.3.g.a	$96$	$3$	96.g	4.b	$2$	$4$	$4$	$2.616$	$\Q(\zeta_{12})$	None		✓	✓	✓	96.3.g.a	$2$	$0$	$0$	$0$	$-8$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{12}^{2}q^{3}+(-2-\zeta_{12}^{3})q^{5}+(\zeta_{12}+\cdots)q^{7}+\cdots$
96.3.h.a	$96$	$3$	96.h	24.h	$2$	$1$	$1$	$2.616$	$\Q$	$\Q(\sqrt{-6}) $	✓				24.3.h.a	$2$	$0$	$0$	$-3$	$2$	$10$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{3}+2q^{5}+10q^{7}+9q^{9}+10q^{11}+\cdots$
96.3.h.b	$96$	$3$	96.h	24.h	$2$	$1$	$1$	$2.616$	$\Q$	$\Q(\sqrt{-6}) $	✓				24.3.h.a	$2$	$0$	$0$	$3$	$-2$	$10$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+3q^{3}-2q^{5}+10q^{7}+9q^{9}-10q^{11}+\cdots$
96.3.h.c	$96$	$3$	96.h	24.h	$2$	$4$	$4$	$2.616$	$\Q(\sqrt{2}, \sqrt{-7})$	None			✓		24.3.h.c	$4$	$0$	$0$	$0$	$0$	$-16$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}-\beta _{2})q^{3}-2\beta _{1}q^{5}-4q^{7}+\cdots$
96.3.m.a	$96$	$3$	96.m	32.h	$8$	$64$	$16$	$2.616$		None		✓	✓	✓	96.3.m.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
96.3.p.a	$96$	$3$	96.p	96.p	$8$	$120$	$30$	$2.616$		None		✓	✓	✓	96.3.p.a	$4$	$0$	$0$	$-4$	$0$	$-8$			$\mathrm{SU}(2)[C_{8}]$
96.4.a.a	$96$	$4$	96.a	1.a	$1$	$1$	$1$	$5.664$	$\Q$	None	✓	✓			96.4.a.a	$1$	$0$	$0$	$-3$	$-14$	$36$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-14q^{5}+6^{2}q^{7}+9q^{9}+6^{2}q^{11}+\cdots$
96.4.a.b	$96$	$4$	96.a	1.a	$1$	$1$	$1$	$5.664$	$\Q$	None	✓	✓	✓	✓	96.4.a.b	$1$	$1$	$0$	$-3$	$2$	$-12$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+2q^{5}-12q^{7}+9q^{9}-60q^{11}+\cdots$
96.4.a.c	$96$	$4$	96.a	1.a	$1$	$1$	$1$	$5.664$	$\Q$	None	✓	✓			96.4.a.c	$1$	$0$	$0$	$-3$	$10$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+10q^{5}-4q^{7}+9q^{9}+20q^{11}+\cdots$
96.4.a.d	$96$	$4$	96.a	1.a	$1$	$1$	$1$	$5.664$	$\Q$	None	✓	✓	✓	✓	96.4.a.a	$1$	$1$	$0$	$3$	$-14$	$-36$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-14q^{5}-6^{2}q^{7}+9q^{9}-6^{2}q^{11}+\cdots$
96.4.a.e	$96$	$4$	96.a	1.a	$1$	$1$	$1$	$5.664$	$\Q$	None	✓	✓			96.4.a.b	$1$	$0$	$0$	$3$	$2$	$12$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+2q^{5}+12q^{7}+9q^{9}+60q^{11}+\cdots$
96.4.a.f	$96$	$4$	96.a	1.a	$1$	$1$	$1$	$5.664$	$\Q$	None	✓	✓			96.4.a.c	$1$	$0$	$0$	$3$	$10$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+10q^{5}+4q^{7}+9q^{9}-20q^{11}+\cdots$
96.4.c.a	$96$	$4$	96.c	12.b	$2$	$12$	$12$	$5.664$	12.0.$\cdots$.1	None		✓	✓	✓	96.4.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{44}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{3}-\beta _{8}q^{5}-\beta _{1}q^{7}+(-2+\beta _{5}+\cdots)q^{9}+\cdots$
96.4.d.a	$96$	$4$	96.d	8.b	$2$	$6$	$6$	$5.664$	6.0.8248384.1	None			✓	✓	24.4.d.a	$2$	$0$	$0$	$0$	$0$	$-28$		$2^{12}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+(-\beta _{2}+\beta _{3})q^{5}+(-5+\beta _{1}+\cdots)q^{7}+\cdots$
96.4.f.a	$96$	$4$	96.f	24.f	$2$	$2$	$2$	$5.664$	$\Q(\sqrt{-2}) $	$\Q(\sqrt{-2}) $					24.4.f.a	$4$	$0$	$0$	$-10$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(-5+\beta )q^{3}+(23-10\beta )q^{9}-50\beta q^{11}+\cdots$
96.4.f.b	$96$	$4$	96.f	24.f	$2$	$8$	$8$	$5.664$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None			✓		24.4.f.b	$4$	$0$	$0$	$12$	$0$	$0$		$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{2})q^{3}+\beta _{4}q^{5}-\beta _{6}q^{7}+(-9+\cdots)q^{9}+\cdots$
96.4.n.a	$96$	$4$	96.n	32.g	$8$	$96$	$24$	$5.664$		None		✓	✓	✓	96.4.n.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
96.4.o.a	$96$	$4$	96.o	96.o	$8$	$184$	$46$	$5.664$		None		✓	✓	✓	96.4.o.a	$4$	$0$	$0$	$-4$	$0$	$-8$			$\mathrm{SU}(2)[C_{8}]$
96.5.b.a	$96$	$5$	96.b	8.d	$2$	$8$	$8$	$9.924$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None			✓	✓	24.5.b.a	$2$	$0$	$0$	$0$	$0$	$0$		$2^{24}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+\beta _{2}q^{5}+(-\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{7}+\cdots$
96.5.e.a	$96$	$5$	96.e	3.b	$2$	$8$	$8$	$9.924$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		✓			96.5.e.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{24}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{2}q^{5}-\beta _{3}q^{7}+(-11-2\beta _{2}+\cdots)q^{9}+\cdots$
96.5.e.b	$96$	$5$	96.e	3.b	$2$	$8$	$8$	$9.924$	8.0.3317760000.8	None		✓			96.5.e.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{24}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+\beta _{2}q^{5}+(\beta _{1}+\beta _{4})q^{7}+(-3+\cdots)q^{9}+\cdots$
96.5.g.a	$96$	$5$	96.g	4.b	$2$	$4$	$4$	$9.924$	$\Q(\zeta_{12})$	None		✓			96.5.g.a	$2$	$0$	$0$	$0$	$-40$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+3\zeta_{12}^{2}q^{3}+(-10-\zeta_{12}^{3})q^{5}+(11\zeta_{12}+\cdots)q^{7}+\cdots$
96.5.g.b	$96$	$5$	96.g	4.b	$2$	$4$	$4$	$9.924$	$\Q(\zeta_{12})$	None		✓			96.5.g.b	$2$	$0$	$0$	$0$	$88$	$0$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{12}^{2}q^{3}+(22-\zeta_{12}^{3})q^{5}+(-\zeta_{12}+\cdots)q^{7}+\cdots$
96.5.h.a	$96$	$5$	96.h	24.h	$2$	$1$	$1$	$9.924$	$\Q$	$\Q(\sqrt{-6}) $	✓				24.5.h.a	$2$	$0$	$0$	$-9$	$-46$	$-2$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-9q^{3}-46q^{5}-2q^{7}+3^{4}q^{9}+142q^{11}+\cdots$
96.5.h.b	$96$	$5$	96.h	24.h	$2$	$1$	$1$	$9.924$	$\Q$	$\Q(\sqrt{-6}) $	✓				24.5.h.a	$2$	$0$	$0$	$9$	$46$	$-2$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+9q^{3}+46q^{5}-2q^{7}+3^{4}q^{9}-142q^{11}+\cdots$
96.5.h.c	$96$	$5$	96.h	24.h	$2$	$12$	$12$	$9.924$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None			✓		24.5.h.c	$4$	$0$	$0$	$0$	$0$	$8$		$2^{38}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{5}+(1-\beta _{4})q^{7}+\cdots$
96.5.m.a	$96$	$5$	96.m	32.h	$8$	$128$	$32$	$9.924$		None		✓	✓	✓	96.5.m.a	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
96.5.p.a	$96$	$5$	96.p	96.p	$8$	$248$	$62$	$9.924$		None		✓	✓	✓	96.5.p.a	$4$	$0$	$0$	$-4$	$0$	$-8$			$\mathrm{SU}(2)[C_{8}]$
96.6.a.a	$96$	$6$	96.a	1.a	$1$	$1$	$1$	$15.397$	$\Q$	None	✓	✓			96.6.a.a	$1$	$0$	$0$	$-9$	$-86$	$-180$	$-$	$1$	$\mathrm{SU}(2)$	$q-9q^{3}-86q^{5}-180q^{7}+3^{4}q^{9}+\cdots$
96.6.a.b	$96$	$6$	96.a	1.a	$1$	$1$	$1$	$15.397$	$\Q$	None	✓	✓			96.6.a.b	$1$	$1$	$0$	$-9$	$-14$	$100$	$+$	$1$	$\mathrm{SU}(2)$	$q-9q^{3}-14q^{5}+10^{2}q^{7}+3^{4}q^{9}+\cdots$
96.6.a.c	$96$	$6$	96.a	1.a	$1$	$1$	$1$	$15.397$	$\Q$	None	✓	✓			96.6.a.c	$1$	$1$	$0$	$-9$	$26$	$-36$	$+$	$1$	$\mathrm{SU}(2)$	$q-9q^{3}+26q^{5}-6^{2}q^{7}+3^{4}q^{9}-180q^{11}+\cdots$
96.6.a.d	$96$	$6$	96.a	1.a	$1$	$1$	$1$	$15.397$	$\Q$	None	✓	✓			96.6.a.a	$1$	$1$	$0$	$9$	$-86$	$180$	$+$	$1$	$\mathrm{SU}(2)$	$q+9q^{3}-86q^{5}+180q^{7}+3^{4}q^{9}+\cdots$
96.6.a.e	$96$	$6$	96.a	1.a	$1$	$1$	$1$	$15.397$	$\Q$	None	✓	✓			96.6.a.b	$1$	$1$	$0$	$9$	$-14$	$-100$	$+$	$1$	$\mathrm{SU}(2)$	$q+9q^{3}-14q^{5}-10^{2}q^{7}+3^{4}q^{9}+\cdots$
96.6.a.f	$96$	$6$	96.a	1.a	$1$	$1$	$1$	$15.397$	$\Q$	None	✓	✓			96.6.a.c	$1$	$0$	$0$	$9$	$26$	$36$	$-$	$1$	$\mathrm{SU}(2)$	$q+9q^{3}+26q^{5}+6^{2}q^{7}+3^{4}q^{9}+180q^{11}+\cdots$
96.6.a.g	$96$	$6$	96.a	1.a	$1$	$2$	$2$	$15.397$	$\Q(\sqrt{31}) $	None	✓	✓	✓		96.6.a.g	$1$	$0$	$0$	$-18$	$36$	$-120$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q-9q^{3}+(18+\beta )q^{5}+(-60-\beta )q^{7}+\cdots$
96.6.a.h	$96$	$6$	96.a	1.a	$1$	$2$	$2$	$15.397$	$\Q(\sqrt{31}) $	None	✓	✓	✓		96.6.a.g	$1$	$0$	$0$	$18$	$36$	$120$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+9q^{3}+(18+\beta )q^{5}+(60+\beta )q^{7}+3^{4}q^{9}+\cdots$
96.6.c.a	$96$	$6$	96.c	12.b	$2$	$20$	$20$	$15.397$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		✓	✓	✓	96.6.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{134}\cdot 3^{14}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+\beta _{6}q^{5}+\beta _{2}q^{7}+(-2-\beta _{7}+\cdots)q^{9}+\cdots$
96.6.d.a	$96$	$6$	96.d	8.b	$2$	$10$	$10$	$15.397$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None			✓	✓	24.6.d.a	$2$	$0$	$0$	$0$	$0$	$196$		$2^{40}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(20+\beta _{4}+\cdots)q^{7}+\cdots$
96.6.f.a	$96$	$6$	96.f	24.f	$2$	$2$	$2$	$15.397$	$\Q(\sqrt{-2}) $	$\Q(\sqrt{-2}) $					24.6.f.a	$4$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(1-11\beta )q^{3}+(-241-22\beta )q^{9}+\cdots$
96.6.f.b	$96$	$6$	96.f	24.f	$2$	$16$	$16$	$15.397$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None			✓		24.6.f.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{62}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}-\beta _{3}q^{5}+\beta _{4}q^{7}+(30+\beta _{7}+\cdots)q^{9}+\cdots$

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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.