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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	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
1053.1.k.a	$1053$	$1$	1053.k	117.k	$6$	$2$	$1$	$0.526$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q+q^{4}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{13}+q^{16}+\cdots$
1053.1.m.a	$1053$	$1$	1053.m	117.m	$6$	$2$	$1$	$0.526$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{4}+\zeta_{6}q^{13}-\zeta_{6}q^{16}+(1-\zeta_{6}^{2}+\cdots)q^{19}+\cdots$
1053.1.n.a	$1053$	$1$	1053.n	117.n	$6$	$2$	$1$	$0.526$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$-1$	$0$	$-1$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{5}-q^{8}+q^{10}-\zeta_{6}^{2}q^{11}+\cdots$
1053.1.n.b	$1053$	$1$	1053.n	117.n	$6$	$2$	$1$	$0.526$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{6}q^{4}+\zeta_{6}q^{13}+\zeta_{6}^{2}q^{16}-\zeta_{6}^{2}q^{25}+\cdots$
1053.1.n.c	$1053$	$1$	1053.n	117.n	$6$	$2$	$1$	$0.526$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$1$	$0$	$1$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{5}+q^{8}+q^{10}+\zeta_{6}^{2}q^{11}+\cdots$
1053.1.n.d	$1053$	$1$	1053.n	117.n	$6$	$4$	$2$	$0.526$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$3$		$q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}^{2}+\zeta_{12}^{4}+\cdots)q^{4}+\cdots$
1053.1.u.a	$1053$	$1$	1053.u	117.u	$6$	$2$	$1$	$0.526$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$4$		$1$		$q+\zeta_{6}^{2}q^{4}+q^{7}-\zeta_{6}q^{13}-\zeta_{6}q^{16}+\cdots$
1053.1.v.a	$1053$	$1$	1053.v	117.v	$6$	$2$	$1$	$0.526$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{4}-\zeta_{6}^{2}q^{13}+q^{16}+(1-\zeta_{6}^{2}+\cdots)q^{19}+\cdots$
1053.1.z.a	$1053$	$1$	1053.z	117.w	$12$	$4$	$1$	$0.526$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\zeta_{12}^{3}q^{4}+(\zeta_{12}-\zeta_{12}^{4})q^{7}+\zeta_{12}q^{13}+\cdots$
1053.1.bb.a	$1053$	$1$	1053.bb	117.y	$12$	$4$	$1$	$0.526$	$\Q(\zeta_{12})$	$D_{4}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$2$		$1$		$q+\zeta_{12}^{5}q^{4}+(-\zeta_{12}-\zeta_{12}^{4})q^{7}-\zeta_{12}^{5}q^{13}+\cdots$
1053.1.be.a	$1053$	$1$	1053.be	117.ab	$12$	$4$	$1$	$0.526$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-4$		$1$		$q+\zeta_{12}q^{4}+(-1+\zeta_{12}^{3})q^{7}-\zeta_{12}^{5}q^{13}+\cdots$
1053.2.a.a	$1053$	$2$	1053.a	1.a	$1$	$1$	$1$	$8.408$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-4$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-4q^{5}+2q^{7}+8q^{10}+\cdots$
1053.2.a.b	$1053$	$2$	1053.a	1.a	$1$	$1$	$1$	$8.408$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$-2$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-2q^{5}+5q^{7}+3q^{8}+2q^{10}+\cdots$
1053.2.a.c	$1053$	$2$	1053.a	1.a	$1$	$1$	$1$	$8.408$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$2$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+2q^{5}+5q^{7}-3q^{8}+2q^{10}+\cdots$
1053.2.a.d	$1053$	$2$	1053.a	1.a	$1$	$1$	$1$	$8.408$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+4q^{5}+2q^{7}+8q^{10}+\cdots$
1053.2.a.e	$1053$	$2$	1053.a	1.a	$1$	$2$	$2$	$8.408$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-1+\beta )q^{4}+(2-\beta )q^{5}+(-1+\cdots)q^{7}+\cdots$
1053.2.a.f	$1053$	$2$	1053.a	1.a	$1$	$2$	$2$	$8.408$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{4}+(-2+\beta )q^{5}+\cdots$
1053.2.a.g	$1053$	$2$	1053.a	1.a	$1$	$3$	$3$	$8.408$	3.3.621.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots$
1053.2.a.h	$1053$	$2$	1053.a	1.a	$1$	$3$	$3$	$8.408$	3.3.621.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$
1053.2.a.i	$1053$	$2$	1053.a	1.a	$1$	$4$	$4$	$8.408$	$\Q(\sqrt{3}, \sqrt{7})$	$_{}$	None	None	✓	$2$	$1$	$0$	$0$	$0$	$-10$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{3}q^{2}-\beta _{2}q^{4}-\beta _{3}q^{5}+(-2+\beta _{2}+\cdots)q^{7}+\cdots$
1053.2.a.j	$1053$	$2$	1053.a	1.a	$1$	$5$	$5$	$8.408$	5.5.403137.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-\beta _{3}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$
1053.2.a.k	$1053$	$2$	1053.a	1.a	$1$	$5$	$5$	$8.408$	5.5.403137.1	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+\beta _{3}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$
1053.2.a.l	$1053$	$2$	1053.a	1.a	$1$	$6$	$6$	$8.408$	6.6.22931361.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{1}-\beta _{4}+\beta _{5})q^{4}+(-1+\cdots)q^{5}+\cdots$
1053.2.a.m	$1053$	$2$	1053.a	1.a	$1$	$6$	$6$	$8.408$	6.6.22931361.1	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{1}-\beta _{4}+\beta _{5})q^{4}+(1+\cdots)q^{5}+\cdots$
1053.2.a.n	$1053$	$2$	1053.a	1.a	$1$	$8$	$8$	$8.408$	8.8.$\cdots$.1	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$0$	$6$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(\beta _{1}-\beta _{7})q^{5}+\cdots$
1053.2.b.a	$1053$	$2$	1053.b	13.b	$2$	$2$	$2$	$8.408$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-2\zeta_{6})q^{2}-q^{4}+(1-2\zeta_{6})q^{5}+\cdots$
1053.2.b.b	$1053$	$2$	1053.b	13.b	$2$	$2$	$2$	$8.408$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-2\zeta_{6})q^{2}-q^{4}+(1-2\zeta_{6})q^{5}+\cdots$
1053.2.b.c	$1053$	$2$	1053.b	13.b	$2$	$2$	$2$	$8.408$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{6}q^{2}-q^{4}+2\zeta_{6}q^{5}-\zeta_{6}q^{7}-\zeta_{6}q^{8}+\cdots$
1053.2.b.d	$1053$	$2$	1053.b	13.b	$2$	$2$	$2$	$8.408$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{6}q^{2}-q^{4}+2\zeta_{6}q^{5}+\zeta_{6}q^{7}-\zeta_{6}q^{8}+\cdots$
1053.2.b.e	$1053$	$2$	1053.b	13.b	$2$	$2$	$2$	$8.408$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+2q^{4}+\zeta_{6}q^{5}-\zeta_{6}q^{7}+\zeta_{6}q^{11}+\cdots$
1053.2.b.f	$1053$	$2$	1053.b	13.b	$2$	$2$	$2$	$8.408$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+2q^{4}+\zeta_{6}q^{5}+\zeta_{6}q^{7}+\zeta_{6}q^{11}+\cdots$
1053.2.b.g	$1053$	$2$	1053.b	13.b	$2$	$4$	$4$	$8.408$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(-2+\beta _{3})q^{4}-\beta _{1}q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots$
1053.2.b.h	$1053$	$2$	1053.b	13.b	$2$	$4$	$4$	$8.408$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(-2+\beta _{3})q^{4}-\beta _{1}q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots$
1053.2.b.i	$1053$	$2$	1053.b	13.b	$2$	$10$	$10$	$8.408$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$3^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{7}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots$
1053.2.b.j	$1053$	$2$	1053.b	13.b	$2$	$10$	$10$	$8.408$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$3^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{7}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
1053.2.b.k	$1053$	$2$	1053.b	13.b	$2$	$12$	$12$	$8.408$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+(-1+\beta _{2})q^{4}-\beta _{4}q^{5}-\beta _{6}q^{7}+\cdots$
1053.2.e.a	$1053$	$2$	1053.e	9.c	$3$	$2$	$1$	$8.408$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$1$	$-1$	$0$	$-2$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots$
1053.2.e.b	$1053$	$2$	1053.e	9.c	$3$	$2$	$1$	$8.408$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$-1$	$0$	$-2$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots$
1053.2.e.c	$1053$	$2$	1053.e	9.c	$3$	$2$	$1$	$8.408$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$1$	$0$	$2$	$-5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{5}+(-5+\cdots)q^{7}+\cdots$
1053.2.e.d	$1053$	$2$	1053.e	9.c	$3$	$2$	$1$	$8.408$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$1$	$0$	$2$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots$
1053.2.e.e	$1053$	$2$	1053.e	9.c	$3$	$4$	$2$	$8.408$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{1}-\beta _{2})q^{2}+(-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
1053.2.e.f	$1053$	$2$	1053.e	9.c	$3$	$4$	$2$	$8.408$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		$2$	$0$	$-1$	$0$	$-5$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots$
1053.2.e.g	$1053$	$2$	1053.e	9.c	$3$	$4$	$2$	$8.408$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$-1$	$0$	$-3$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
1053.2.e.h	$1053$	$2$	1053.e	9.c	$3$	$4$	$2$	$8.408$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$-1$	$0$	$3$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
1053.2.e.i	$1053$	$2$	1053.e	9.c	$3$	$4$	$2$	$8.408$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{4}-2\zeta_{12}q^{7}+\cdots$
1053.2.e.j	$1053$	$2$	1053.e	9.c	$3$	$4$	$2$	$8.408$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		$2$	$0$	$1$	$0$	$5$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots$
1053.2.e.k	$1053$	$2$	1053.e	9.c	$3$	$4$	$2$	$8.408$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$1$	$0$	$-3$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
1053.2.e.l	$1053$	$2$	1053.e	9.c	$3$	$4$	$2$	$8.408$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$1$	$0$	$3$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
1053.2.e.m	$1053$	$2$	1053.e	9.c	$3$	$4$	$2$	$8.408$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{1}+\beta _{2})q^{2}+(2\beta _{1}+\beta _{2}+2\beta _{3})q^{4}+\cdots$
1053.2.e.n	$1053$	$2$	1053.e	9.c	$3$	$6$	$3$	$8.408$	6.0.1156923.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$-3$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{2}+(-\beta _{1}+\beta _{2}-2\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$

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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.