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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
2288.1.m.a	$2288$	$1$	2288.m	143.d	$2$	$2$	$2$	$1.142$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-143}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$-1$		$1$		$q+\beta q^{3}+(-1+\beta )q^{7}+\beta q^{9}+q^{11}+\cdots$
2288.1.m.b	$2288$	$1$	2288.m	143.d	$2$	$2$	$2$	$1.142$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-143}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$1$		$1$		$q+\beta q^{3}+(1-\beta )q^{7}+\beta q^{9}-q^{11}+q^{13}+\cdots$
2288.1.m.c	$2288$	$1$	2288.m	143.d	$2$	$4$	$4$	$1.142$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$-4$	$0$	$0$		$1$		$q-q^{3}+\zeta_{8}^{2}q^{5}-\zeta_{8}^{2}q^{11}-\zeta_{8}q^{13}+\cdots$
2288.1.z.a	$2288$	$1$	2288.z	2288.z	$4$	$4$	$2$	$1.142$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-143}) $	None		$8$	$0$	$0$	$4$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}+(1+\zeta_{8}^{2})q^{3}-\zeta_{8}^{2}q^{4}+\cdots$
2288.1.z.b	$2288$	$1$	2288.z	2288.z	$4$	$16$	$8$	$1.142$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-143}) $	None		$8$	$0$	$0$	$-4$	$0$	$0$		$1$		$q-\zeta_{40}^{11}q^{2}+(-\zeta_{40}^{14}+\zeta_{40}^{16}+\cdots)q^{3}+\cdots$
2288.1.cq.a	$2288$	$1$	2288.cq	572.aa	$10$	$8$	$2$	$1.142$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-13}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{20}+\zeta_{20}^{7})q^{7}-\zeta_{20}^{2}q^{9}-\zeta_{20}^{9}q^{11}+\cdots$
2288.2.a.a	$2288$	$2$	2288.a	1.a	$1$	$1$	$1$	$18.270$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+3q^{5}+3q^{7}+6q^{9}-q^{11}+\cdots$
2288.2.a.b	$2288$	$2$	2288.a	1.a	$1$	$1$	$1$	$18.270$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}-q^{7}+q^{9}+q^{11}-q^{13}+\cdots$
2288.2.a.c	$2288$	$2$	2288.a	1.a	$1$	$1$	$1$	$18.270$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+3q^{7}+q^{9}-q^{11}+q^{13}+\cdots$
2288.2.a.d	$2288$	$2$	2288.a	1.a	$1$	$1$	$1$	$18.270$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+3q^{5}-q^{7}+q^{9}+q^{11}-q^{13}+\cdots$
2288.2.a.e	$2288$	$2$	2288.a	1.a	$1$	$1$	$1$	$18.270$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+2q^{7}-2q^{9}-q^{11}-q^{13}+\cdots$
2288.2.a.f	$2288$	$2$	2288.a	1.a	$1$	$1$	$1$	$18.270$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+2q^{7}-2q^{9}-q^{11}+q^{13}+\cdots$
2288.2.a.g	$2288$	$2$	2288.a	1.a	$1$	$1$	$1$	$18.270$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}-2q^{7}-2q^{9}-q^{11}+\cdots$
2288.2.a.h	$2288$	$2$	2288.a	1.a	$1$	$1$	$1$	$18.270$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-3$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}+5q^{7}-2q^{9}+q^{11}+\cdots$
2288.2.a.i	$2288$	$2$	2288.a	1.a	$1$	$1$	$1$	$18.270$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-q^{7}-2q^{9}+q^{11}-q^{13}+\cdots$
2288.2.a.j	$2288$	$2$	2288.a	1.a	$1$	$1$	$1$	$18.270$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+2q^{7}-2q^{9}+q^{11}-q^{13}+\cdots$
2288.2.a.k	$2288$	$2$	2288.a	1.a	$1$	$1$	$1$	$18.270$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-3q^{7}-2q^{9}-q^{11}+q^{13}+\cdots$
2288.2.a.l	$2288$	$2$	2288.a	1.a	$1$	$1$	$1$	$18.270$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+3q^{5}+q^{7}+q^{9}+q^{11}+q^{13}+\cdots$
2288.2.a.m	$2288$	$2$	2288.a	1.a	$1$	$2$	$2$	$18.270$	$\Q(\sqrt{21}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-4$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}-2q^{5}+(-1-\beta )q^{7}+(2+\beta )q^{9}+\cdots$
2288.2.a.n	$2288$	$2$	2288.a	1.a	$1$	$2$	$2$	$18.270$	$\Q(\sqrt{21}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$4$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}+2q^{5}+(-3+\beta )q^{7}+(2+\beta )q^{9}+\cdots$
2288.2.a.o	$2288$	$2$	2288.a	1.a	$1$	$2$	$2$	$18.270$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$3$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-2\beta q^{5}-\beta q^{7}+(-1+3\beta )q^{9}+\cdots$
2288.2.a.p	$2288$	$2$	2288.a	1.a	$1$	$2$	$2$	$18.270$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-2+2\beta )q^{5}+(-2+3\beta )q^{7}+\cdots$
2288.2.a.q	$2288$	$2$	2288.a	1.a	$1$	$2$	$2$	$18.270$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$-2$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(-2+2\beta )q^{5}+(2+\beta )q^{7}+\cdots$
2288.2.a.r	$2288$	$2$	2288.a	1.a	$1$	$2$	$2$	$18.270$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(2-\beta )q^{7}+(1+3\beta )q^{9}+\cdots$
2288.2.a.s	$2288$	$2$	2288.a	1.a	$1$	$3$	$3$	$18.270$	3.3.229.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$1$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{3}+(\beta _{1}-\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots$
2288.2.a.t	$2288$	$2$	2288.a	1.a	$1$	$3$	$3$	$18.270$	3.3.961.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(2-\beta _{1}+\beta _{2})q^{7}+\cdots$
2288.2.a.u	$2288$	$2$	2288.a	1.a	$1$	$3$	$3$	$18.270$	3.3.229.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-5$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(-2+\beta _{1}-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots$
2288.2.a.v	$2288$	$2$	2288.a	1.a	$1$	$3$	$3$	$18.270$	3.3.229.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(1-\beta _{2})q^{7}+\cdots$
2288.2.a.w	$2288$	$2$	2288.a	1.a	$1$	$3$	$3$	$18.270$	3.3.229.1	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-1$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(2+2\beta _{1}+\cdots)q^{7}+\cdots$
2288.2.a.x	$2288$	$2$	2288.a	1.a	$1$	$4$	$4$	$18.270$	4.4.1957.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$-6$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+(-2+\beta _{3})q^{7}+\cdots$
2288.2.a.y	$2288$	$2$	2288.a	1.a	$1$	$5$	$5$	$18.270$	5.5.7698829.1	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-4$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$
2288.2.a.z	$2288$	$2$	2288.a	1.a	$1$	$6$	$6$	$18.270$	6.6.194616205.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$1$	$-4$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{3}+\beta _{4}q^{5}+(-1-\beta _{5})q^{7}+\cdots$
2288.2.a.ba	$2288$	$2$	2288.a	1.a	$1$	$6$	$6$	$18.270$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$5$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+(1-\beta _{2})q^{5}-\beta _{5}q^{7}+(2+\beta _{4}+\cdots)q^{9}+\cdots$
2288.2.b.a	$2288$	$2$	2288.b	572.b	$2$	$4$	$4$	$18.270$	$\Q(\sqrt{2}, \sqrt{-13})$	$_{}$	$\Q(\sqrt{-13}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+(2\beta _{1}+\beta _{2})q^{7}+3q^{9}+(\beta _{1}+2\beta _{2}+\cdots)q^{11}+\cdots$
2288.2.b.b	$2288$	$2$	2288.b	572.b	$2$	$24$	$24$	$18.270$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2288.2.b.c	$2288$	$2$	2288.b	572.b	$2$	$56$	$56$	$18.270$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
2288.2.i.a	$2288$	$2$	2288.i	44.c	$2$	$24$	$24$	$18.270$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-12$	$0$			$\mathrm{SU}(2)[C_{2}]$
2288.2.i.b	$2288$	$2$	2288.i	44.c	$2$	$48$	$48$	$18.270$		$_{}$	None	None		$4$	$0$	$0$	$0$	$12$	$0$			$\mathrm{SU}(2)[C_{2}]$
2288.2.j.a	$2288$	$2$	2288.j	13.b	$2$	$2$	$2$	$18.270$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$-6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-3q^{3}-iq^{5}-iq^{7}+6q^{9}-iq^{11}+\cdots$
2288.2.j.b	$2288$	$2$	2288.j	13.b	$2$	$2$	$2$	$18.270$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-4iq^{7}-3q^{9}+iq^{11}+(-3+2i)q^{13}+\cdots$
2288.2.j.c	$2288$	$2$	2288.j	13.b	$2$	$2$	$2$	$18.270$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{5}-4iq^{7}-3q^{9}-iq^{11}+(-2+\cdots)q^{13}+\cdots$
2288.2.j.d	$2288$	$2$	2288.j	13.b	$2$	$2$	$2$	$18.270$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3iq^{5}-iq^{7}-3q^{9}+iq^{11}+(3+\cdots)q^{13}+\cdots$
2288.2.j.e	$2288$	$2$	2288.j	13.b	$2$	$2$	$2$	$18.270$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{5}+iq^{7}-3q^{9}-iq^{11}+(3-2i)q^{13}+\cdots$
2288.2.j.f	$2288$	$2$	2288.j	13.b	$2$	$4$	$4$	$18.270$	$\Q(i, \sqrt{21})$	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{3})q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(3+\cdots)q^{9}+\cdots$
2288.2.j.g	$2288$	$2$	2288.j	13.b	$2$	$4$	$4$	$18.270$	$\Q(i, \sqrt{17})$	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{3})q^{3}-\beta _{2}q^{5}+(2\beta _{1}+\beta _{2})q^{7}+\cdots$
2288.2.j.h	$2288$	$2$	2288.j	13.b	$2$	$6$	$6$	$18.270$	6.0.301925376.1	$_{}$	None	None		$2$	$0$	$0$	$6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+\beta _{2}q^{5}+(\beta _{3}+\beta _{4})q^{7}-2q^{9}+\cdots$
2288.2.j.i	$2288$	$2$	2288.j	13.b	$2$	$8$	$8$	$18.270$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+(\beta _{1}+\beta _{5}+\beta _{6}-\beta _{7})q^{5}+\cdots$
2288.2.j.j	$2288$	$2$	2288.j	13.b	$2$	$10$	$10$	$18.270$	10.0.$\cdots$.2	$_{}$	None	None		$2$	$0$	$0$	$-4$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+(\beta _{7}+\beta _{8})q^{5}+(\beta _{4}-\beta _{5}-\beta _{7}+\cdots)q^{7}+\cdots$
2288.2.j.k	$2288$	$2$	2288.j	13.b	$2$	$12$	$12$	$18.270$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$4$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+(\beta _{4}+\beta _{6})q^{5}+(\beta _{2}+\beta _{4})q^{7}+\cdots$
2288.2.j.l	$2288$	$2$	2288.j	13.b	$2$	$16$	$16$	$18.270$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-6$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}+(\beta _{7}-\beta _{14})q^{5}+\beta _{15}q^{7}+\cdots$

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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.