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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 94 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
1071.1.h.a	$1071$	$1$	1071.h	119.d	$2$	$2$	$2$	$0.534$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-119}) $	None	✓	$2$	$0$	$1$	$0$	$-1$	$-2$		$1$		$q+\beta q^{2}+\beta q^{4}+(-1+\beta )q^{5}-q^{7}+\cdots$
1071.1.h.b	$1071$	$1$	1071.h	119.d	$2$	$2$	$2$	$0.534$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-119}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$2$		$1$		$q+\beta q^{2}+\beta q^{4}+(1-\beta )q^{5}+q^{7}+q^{8}+\cdots$
1071.1.x.a	$1071$	$1$	1071.x	1071.x	$6$	$2$	$1$	$0.534$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$1$	$-1$	$1$	$-1$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}+\zeta_{6}q^{5}-q^{6}+\zeta_{6}^{2}q^{7}+\cdots$
1071.1.x.b	$1071$	$1$	1071.x	1071.x	$6$	$2$	$1$	$0.534$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$1$	$1$	$-1$	$1$		$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{5}+q^{6}-\zeta_{6}^{2}q^{7}+\cdots$
1071.1.x.c	$1071$	$1$	1071.x	1071.x	$6$	$8$	$4$	$0.534$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$-1$	$-1$	$1$	$4$		$1$		$q+(-\zeta_{30}-\zeta_{30}^{9})q^{2}+\zeta_{30}q^{3}+(\zeta_{30}^{2}+\cdots)q^{4}+\cdots$
1071.1.x.d	$1071$	$1$	1071.x	1071.x	$6$	$8$	$4$	$0.534$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$-1$	$1$	$-1$	$-4$		$1$		$q+(-\zeta_{30}^{3}-\zeta_{30}^{7})q^{2}-\zeta_{30}^{7}q^{3}+\cdots$
1071.1.ci.a	$1071$	$1$	1071.ci	1071.bi	$12$	$8$	$2$	$0.534$	$\Q(\zeta_{24})$	$S_{4}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{5}q^{3}+\zeta_{24}^{5}q^{5}+\cdots$
1071.2.a.a	$1071$	$2$	1071.a	1.a	$1$	$1$	$1$	$8.552$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-q^{5}-q^{7}+2q^{10}+\cdots$
1071.2.a.b	$1071$	$2$	1071.a	1.a	$1$	$1$	$1$	$8.552$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{5}-q^{7}-3q^{11}+3q^{13}+\cdots$
1071.2.a.c	$1071$	$2$	1071.a	1.a	$1$	$1$	$1$	$8.552$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{5}+q^{7}+5q^{11}-5q^{13}+\cdots$
1071.2.a.d	$1071$	$2$	1071.a	1.a	$1$	$1$	$1$	$8.552$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+3q^{5}+q^{7}+6q^{10}+\cdots$
1071.2.a.e	$1071$	$2$	1071.a	1.a	$1$	$2$	$2$	$8.552$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1-\beta )q^{5}-q^{7}-2\beta q^{8}+(-2+\cdots)q^{10}+\cdots$
1071.2.a.f	$1071$	$2$	1071.a	1.a	$1$	$2$	$2$	$8.552$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+(2+2\beta )q^{4}+(2-\beta )q^{5}+\cdots$
1071.2.a.g	$1071$	$2$	1071.a	1.a	$1$	$3$	$3$	$8.552$	3.3.148.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-5$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots$
1071.2.a.h	$1071$	$2$	1071.a	1.a	$1$	$3$	$3$	$8.552$	3.3.316.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$-2$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{1})q^{5}+\cdots$
1071.2.a.i	$1071$	$2$	1071.a	1.a	$1$	$3$	$3$	$8.552$	3.3.148.1	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$5$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots$
1071.2.a.j	$1071$	$2$	1071.a	1.a	$1$	$4$	$4$	$8.552$	4.4.7232.1	$_{}$	None	None	✓	$1$	$0$	$-2$	$0$	$2$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(1-\beta _{2}-\beta _{3})q^{4}-\beta _{1}q^{5}+\cdots$
1071.2.a.k	$1071$	$2$	1071.a	1.a	$1$	$4$	$4$	$8.552$	4.4.9301.1	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots$
1071.2.a.l	$1071$	$2$	1071.a	1.a	$1$	$5$	$5$	$8.552$	5.5.1224176.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-3$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-1+\beta _{3}+\cdots)q^{5}+\cdots$
1071.2.a.m	$1071$	$2$	1071.a	1.a	$1$	$5$	$5$	$8.552$	5.5.453749.1	$_{}$	None	None	✓	$1$	$0$	$-2$	$0$	$0$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{2}+(2-\beta _{3})q^{4}+(1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
1071.2.a.n	$1071$	$2$	1071.a	1.a	$1$	$5$	$5$	$8.552$	5.5.1224176.1	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$3$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots$
1071.2.c.a	$1071$	$2$	1071.c	357.c	$2$	$48$	$48$	$8.552$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1071.2.d.a	$1071$	$2$	1071.d	21.c	$2$	$4$	$4$	$8.552$	$\Q(\sqrt{-2}, \sqrt{-5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q+2q^{4}+(-1-\beta _{1}-\beta _{2})q^{5}-\beta _{2}q^{7}+\cdots$
1071.2.d.b	$1071$	$2$	1071.d	21.c	$2$	$4$	$4$	$8.552$	$\Q(\sqrt{-2}, \sqrt{-5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$0$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q+2q^{4}+(1+\beta _{1}+\beta _{2})q^{5}-\beta _{1}q^{7}+\cdots$
1071.2.d.c	$1071$	$2$	1071.d	21.c	$2$	$16$	$16$	$8.552$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{14}q^{5}+\cdots$
1071.2.d.d	$1071$	$2$	1071.d	21.c	$2$	$16$	$16$	$8.552$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}-\beta _{14}q^{5}+\cdots$
1071.2.f.a	$1071$	$2$	1071.f	17.b	$2$	$6$	$6$	$8.552$	6.0.350464.1	$_{}$	None	None		$2$	$0$	$-4$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{2})q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots$
1071.2.f.b	$1071$	$2$	1071.f	17.b	$2$	$10$	$10$	$8.552$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+(2-\beta _{8})q^{4}+(\beta _{2}-\beta _{7}+\beta _{9})q^{5}+\cdots$
1071.2.f.c	$1071$	$2$	1071.f	17.b	$2$	$10$	$10$	$8.552$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+(-\beta _{2}-\beta _{3})q^{4}+(\beta _{5}+\beta _{7}+\cdots)q^{5}+\cdots$
1071.2.f.d	$1071$	$2$	1071.f	17.b	$2$	$20$	$20$	$8.552$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{11}q^{2}+(2-\beta _{13})q^{4}-\beta _{4}q^{5}-\beta _{3}q^{7}+\cdots$
1071.2.i.a	$1071$	$2$	1071.i	7.c	$3$	$2$	$1$	$8.552$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-1$	$0$	$1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots$
1071.2.i.b	$1071$	$2$	1071.i	7.c	$3$	$2$	$1$	$8.552$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{4}+4\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots$
1071.2.i.c	$1071$	$2$	1071.i	7.c	$3$	$2$	$1$	$8.552$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$1$	$0$	$3$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+3\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots$
1071.2.i.d	$1071$	$2$	1071.i	7.c	$3$	$6$	$3$	$8.552$	6.0.64827.1	$_{}$	None	None		$2$	$0$	$-1$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{4}+\cdots$
1071.2.i.e	$1071$	$2$	1071.i	7.c	$3$	$8$	$4$	$8.552$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		$2$	$0$	$-3$	$0$	$-6$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{4})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
1071.2.i.f	$1071$	$2$	1071.i	7.c	$3$	$8$	$4$	$8.552$	8.0.1767277521.3	$_{}$	None	None		$2$	$0$	$-1$	$0$	$4$	$7$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{3}-\beta _{7})q^{2}+(\beta _{4}+\beta _{5}-2\beta _{6}+\cdots)q^{4}+\cdots$
1071.2.i.g	$1071$	$2$	1071.i	7.c	$3$	$10$	$5$	$8.552$	10.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$-2$	$0$	$1$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{6})q^{2}+(-2+\beta _{3}+2\beta _{4}+\cdots)q^{4}+\cdots$
1071.2.i.h	$1071$	$2$	1071.i	7.c	$3$	$12$	$6$	$8.552$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$2$	$0$	$-7$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{5}-\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots$
1071.2.i.i	$1071$	$2$	1071.i	7.c	$3$	$14$	$7$	$8.552$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		$2$	$0$	$3$	$0$	$2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{2})q^{2}+(-1-\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots$
1071.2.i.j	$1071$	$2$	1071.i	7.c	$3$	$22$	$11$	$8.552$		$_{}$	None	None		$2$	$0$	$-4$	$0$	$0$	$3$			$\mathrm{SU}(2)[C_{3}]$
1071.2.i.k	$1071$	$2$	1071.i	7.c	$3$	$22$	$11$	$8.552$		$_{}$	None	None		$2$	$0$	$4$	$0$	$0$	$3$			$\mathrm{SU}(2)[C_{3}]$
1071.2.j.a	$1071$	$2$	1071.j	9.c	$3$	$2$	$1$	$8.552$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-1$	$3$	$-2$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
1071.2.j.b	$1071$	$2$	1071.j	9.c	$3$	$2$	$1$	$8.552$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$1$	$3$	$0$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
1071.2.j.c	$1071$	$2$	1071.j	9.c	$3$	$36$	$18$	$8.552$		$_{}$	None	None		$2$	$0$	$-1$	$-2$	$1$	$18$			$\mathrm{SU}(2)[C_{3}]$
1071.2.j.d	$1071$	$2$	1071.j	9.c	$3$	$36$	$18$	$8.552$		$_{}$	None	None		$2$	$0$	$1$	$-2$	$-1$	$-18$			$\mathrm{SU}(2)[C_{3}]$
1071.2.j.e	$1071$	$2$	1071.j	9.c	$3$	$58$	$29$	$8.552$		$_{}$	None	None		$2$	$0$	$-2$	$1$	$-1$	$29$			$\mathrm{SU}(2)[C_{3}]$
1071.2.j.f	$1071$	$2$	1071.j	9.c	$3$	$58$	$29$	$8.552$		$_{}$	None	None		$2$	$0$	$2$	$1$	$-1$	$-29$			$\mathrm{SU}(2)[C_{3}]$
1071.2.n.a	$1071$	$2$	1071.n	17.c	$4$	$12$	$6$	$8.552$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-8$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{10}q^{2}+(1-\beta _{2}+\beta _{7}-\beta _{8})q^{4}+\cdots$
1071.2.n.b	$1071$	$2$	1071.n	17.c	$4$	$20$	$10$	$8.552$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-8$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+(-1-\beta _{7}+\beta _{8})q^{4}+(\beta _{10}+\cdots)q^{5}+\cdots$
1071.2.n.c	$1071$	$2$	1071.n	17.c	$4$	$20$	$10$	$8.552$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$8$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+(-2+\beta _{12}+\beta _{13})q^{4}+(1+\cdots)q^{5}+\cdots$

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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.