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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 77 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1190.2.a.a	$1190$	$2$	1190.a	1.a	$1$	$1$	$1$	$9.502$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}-3q^{9}+\cdots$
1190.2.a.b	$1190$	$2$	1190.a	1.a	$1$	$1$	$1$	$9.502$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
1190.2.a.c	$1190$	$2$	1190.a	1.a	$1$	$1$	$1$	$9.502$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
1190.2.a.d	$1190$	$2$	1190.a	1.a	$1$	$1$	$1$	$9.502$	$\Q$	None	✓	$1$	$1$	$1$	$-3$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}-q^{7}+\cdots$
1190.2.a.e	$1190$	$2$	1190.a	1.a	$1$	$1$	$1$	$9.502$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
1190.2.a.f	$1190$	$2$	1190.a	1.a	$1$	$1$	$1$	$9.502$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-3q^{9}+\cdots$
1190.2.a.g	$1190$	$2$	1190.a	1.a	$1$	$2$	$2$	$9.502$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$-2$	$-1$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta q^{3}+q^{4}-q^{5}+\beta q^{6}-q^{7}+\cdots$
1190.2.a.h	$1190$	$2$	1190.a	1.a	$1$	$2$	$2$	$9.502$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$1$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}-q^{7}+\cdots$
1190.2.a.i	$1190$	$2$	1190.a	1.a	$1$	$2$	$2$	$9.502$	$\Q(\sqrt{21}) $	None	✓	$1$	$0$	$2$	$1$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}-q^{5}+\beta q^{6}-q^{7}+\cdots$
1190.2.a.j	$1190$	$2$	1190.a	1.a	$1$	$3$	$3$	$9.502$	3.3.2597.1	None	✓	$1$	$0$	$-3$	$-1$	$3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
1190.2.a.k	$1190$	$2$	1190.a	1.a	$1$	$3$	$3$	$9.502$	3.3.3229.1	None	✓	$1$	$0$	$-3$	$-1$	$3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
1190.2.a.l	$1190$	$2$	1190.a	1.a	$1$	$3$	$3$	$9.502$	3.3.837.1	None	✓	$1$	$0$	$-3$	$0$	$-3$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
1190.2.a.m	$1190$	$2$	1190.a	1.a	$1$	$3$	$3$	$9.502$	3.3.229.1	None	✓	$1$	$0$	$3$	$3$	$3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+q^{5}+(1-\beta _{1}+\cdots)q^{6}+\cdots$
1190.2.a.n	$1190$	$2$	1190.a	1.a	$1$	$4$	$4$	$9.502$	4.4.109621.1	None	✓	$1$	$0$	$4$	$2$	$-4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{1})q^{3}+q^{4}-q^{5}+(1-\beta _{1}+\cdots)q^{6}+\cdots$
1190.2.a.o	$1190$	$2$	1190.a	1.a	$1$	$5$	$5$	$9.502$	5.5.9251432.1	None	✓	$1$	$0$	$5$	$2$	$5$	$5$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots$
1190.2.c.a	$1190$	$2$	1190.c	17.b	$2$	$2$	$2$	$9.502$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+2iq^{3}+q^{4}-iq^{5}-2iq^{6}+\cdots$
1190.2.c.b	$1190$	$2$	1190.c	17.b	$2$	$2$	$2$	$9.502$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+iq^{3}+q^{4}+iq^{5}-iq^{6}+iq^{7}+\cdots$
1190.2.c.c	$1190$	$2$	1190.c	17.b	$2$	$2$	$2$	$9.502$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+iq^{5}-iq^{7}+q^{8}+3q^{9}+\cdots$
1190.2.c.d	$1190$	$2$	1190.c	17.b	$2$	$4$	$4$	$9.502$	$\Q(i, \sqrt{13})$	None		$2$	$0$	$-4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots$
1190.2.c.e	$1190$	$2$	1190.c	17.b	$2$	$4$	$4$	$9.502$	$\Q(i, \sqrt{13})$	None		$2$	$0$	$-4$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}-\beta _{1}q^{5}+\beta _{1}q^{7}-q^{8}+\cdots$
1190.2.c.f	$1190$	$2$	1190.c	17.b	$2$	$4$	$4$	$9.502$	$\Q(i, \sqrt{17})$	None		$2$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots$
1190.2.c.g	$1190$	$2$	1190.c	17.b	$2$	$4$	$4$	$9.502$	$\Q(i, \sqrt{13})$	None		$2$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots$
1190.2.c.h	$1190$	$2$	1190.c	17.b	$2$	$6$	$6$	$9.502$	6.0.14077504.1	None		$2$	$0$	$6$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+(\beta _{1}+\beta _{2})q^{3}+q^{4}-\beta _{2}q^{5}+\cdots$
1190.2.c.i	$1190$	$2$	1190.c	17.b	$2$	$8$	$8$	$9.502$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$-8$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta _{7}q^{3}+q^{4}+\beta _{4}q^{5}-\beta _{7}q^{6}+\cdots$
1190.2.e.a	$1190$	$2$	1190.e	5.b	$2$	$2$	$2$	$9.502$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}+iq^{3}-q^{4}+(-1-2i)q^{5}+\cdots$
1190.2.e.b	$1190$	$2$	1190.e	5.b	$2$	$2$	$2$	$9.502$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}+iq^{3}-q^{4}+(-1-2i)q^{5}+\cdots$
1190.2.e.c	$1190$	$2$	1190.e	5.b	$2$	$4$	$4$	$9.502$	$\Q(\zeta_{8})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}^{2}q^{2}+(-\zeta_{8}+2\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\cdots$
1190.2.e.d	$1190$	$2$	1190.e	5.b	$2$	$4$	$4$	$9.502$	$\Q(i, \sqrt{5})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+\beta _{1}q^{3}-q^{4}+(2\beta _{1}+\beta _{3})q^{5}+\cdots$
1190.2.e.e	$1190$	$2$	1190.e	5.b	$2$	$10$	$10$	$9.502$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+(\beta _{1}+\beta _{3})q^{3}-q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots$
1190.2.e.f	$1190$	$2$	1190.e	5.b	$2$	$12$	$12$	$9.502$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{9}q^{5}-\beta _{2}q^{6}+\cdots$
1190.2.e.g	$1190$	$2$	1190.e	5.b	$2$	$14$	$14$	$9.502$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None		$2$	$0$	$0$	$0$	$-2$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{11}q^{5}+\beta _{6}q^{6}+\cdots$
1190.2.g.a	$1190$	$2$	1190.g	85.c	$2$	$4$	$4$	$9.502$	$\Q(i, \sqrt{21})$	None		$2$	$0$	$0$	$-2$	$-4$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(-1+\beta _{3})q^{3}-q^{4}+(-1+\cdots)q^{5}+\cdots$
1190.2.g.b	$1190$	$2$	1190.g	85.c	$2$	$4$	$4$	$9.502$	$\Q(i, \sqrt{21})$	None		$2$	$0$	$0$	$2$	$4$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(1-\beta _{3})q^{3}-q^{4}+(1-2\beta _{2}+\cdots)q^{5}+\cdots$
1190.2.g.c	$1190$	$2$	1190.g	85.c	$2$	$24$	$24$	$9.502$		None		$2$	$0$	$0$	$-10$	$-4$	$-24$			$\mathrm{SU}(2)[C_{2}]$
1190.2.g.d	$1190$	$2$	1190.g	85.c	$2$	$24$	$24$	$9.502$		None		$2$	$0$	$0$	$10$	$4$	$24$			$\mathrm{SU}(2)[C_{2}]$
1190.2.i.a	$1190$	$2$	1190.i	7.c	$3$	$2$	$1$	$9.502$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$-2$	$1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
1190.2.i.b	$1190$	$2$	1190.i	7.c	$3$	$2$	$1$	$9.502$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$-1$	$1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
1190.2.i.c	$1190$	$2$	1190.i	7.c	$3$	$2$	$1$	$9.502$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots$
1190.2.i.d	$1190$	$2$	1190.i	7.c	$3$	$2$	$1$	$9.502$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$1$	$-1$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
1190.2.i.e	$1190$	$2$	1190.i	7.c	$3$	$2$	$1$	$9.502$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$1$	$1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
1190.2.i.f	$1190$	$2$	1190.i	7.c	$3$	$2$	$1$	$9.502$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$-1$	$-1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
1190.2.i.g	$1190$	$2$	1190.i	7.c	$3$	$2$	$1$	$9.502$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$-1$	$-1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
1190.2.i.h	$1190$	$2$	1190.i	7.c	$3$	$4$	$2$	$9.502$	$\Q(\sqrt{2}, \sqrt{-3})$	None		$2$	$0$	$2$	$-4$	$2$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{2})q^{2}+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{3}+\cdots$
1190.2.i.i	$1190$	$2$	1190.i	7.c	$3$	$4$	$2$	$9.502$	$\Q(\sqrt{-3}, \sqrt{17})$	None		$2$	$0$	$2$	$-1$	$-2$	$8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{2})q^{2}-\beta _{1}q^{3}-\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots$
1190.2.i.j	$1190$	$2$	1190.i	7.c	$3$	$8$	$4$	$9.502$	8.0.$\cdots$.16	None		$2$	$0$	$-4$	$2$	$-4$	$8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{3}q^{2}+\beta _{1}q^{3}+(-1+\beta _{3})q^{4}-\beta _{3}q^{5}+\cdots$
1190.2.i.k	$1190$	$2$	1190.i	7.c	$3$	$8$	$4$	$9.502$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$-4$	$2$	$4$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{4})q^{2}+(\beta _{4}-\beta _{6})q^{3}-\beta _{4}q^{4}+\cdots$
1190.2.i.l	$1190$	$2$	1190.i	7.c	$3$	$8$	$4$	$9.502$	8.0.$\cdots$.13	None		$2$	$0$	$4$	$2$	$4$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{5})q^{2}+\beta _{1}q^{3}+\beta _{5}q^{4}+(1+\beta _{5}+\cdots)q^{5}+\cdots$
1190.2.i.m	$1190$	$2$	1190.i	7.c	$3$	$8$	$4$	$9.502$	8.0.$\cdots$.3	None		$2$	$0$	$4$	$2$	$4$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{4})q^{2}+(-\beta _{1}-\beta _{4})q^{3}+\beta _{4}q^{4}+\cdots$
1190.2.i.n	$1190$	$2$	1190.i	7.c	$3$	$12$	$6$	$9.502$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$6$	$1$	$-6$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{7})q^{2}+\beta _{1}q^{3}+\beta _{7}q^{4}+(-1+\cdots)q^{5}+\cdots$
1190.2.i.o	$1190$	$2$	1190.i	7.c	$3$	$14$	$7$	$9.502$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None		$2$	$0$	$-7$	$-1$	$-7$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{4})q^{2}+(\beta _{1}-\beta _{2})q^{3}-\beta _{4}q^{4}+\cdots$

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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.