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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 113 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
1176.1.e.a	$1176$	$1$	1176.e	168.e	$2$	$8$	$8$	$0.587$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{16}^{4}q^{2}-\zeta_{16}q^{3}-q^{4}+\zeta_{16}^{5}q^{6}+\cdots$
1176.1.n.a	$1176$	$1$	1176.n	24.h	$2$	$1$	$1$	$0.587$	$\Q$	$D_{3}$	$\Q(\sqrt{-6}) $	None	✓	$2$	$0$	$-1$	$-1$	$1$	$0$		$1$		$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots$
1176.1.n.b	$1176$	$1$	1176.n	24.h	$2$	$1$	$1$	$0.587$	$\Q$	$D_{3}$	$\Q(\sqrt{-6}) $	None	✓	$2$	$0$	$-1$	$1$	$-1$	$0$		$1$		$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
1176.1.n.c	$1176$	$1$	1176.n	24.h	$2$	$1$	$1$	$0.587$	$\Q$	$D_{3}$	$\Q(\sqrt{-6}) $	None	✓	$2$	$0$	$1$	$-1$	$1$	$0$		$1$		$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
1176.1.n.d	$1176$	$1$	1176.n	24.h	$2$	$1$	$1$	$0.587$	$\Q$	$D_{3}$	$\Q(\sqrt{-6}) $	None	✓	$2$	$0$	$1$	$1$	$-1$	$0$		$1$		$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
1176.1.n.e	$1176$	$1$	1176.n	24.h	$2$	$4$	$4$	$0.587$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+(\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{5}+\cdots$
1176.1.s.a	$1176$	$1$	1176.s	168.s	$6$	$2$	$1$	$0.587$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$-1$	$1$	$-1$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\cdots$
1176.1.s.b	$1176$	$1$	1176.s	168.s	$6$	$2$	$1$	$0.587$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$1$	$-1$	$1$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots$
1176.1.s.c	$1176$	$1$	1176.s	168.s	$6$	$8$	$4$	$0.587$	$\Q(\zeta_{24})$	$D_{4}$	$\Q(\sqrt{-14}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{5}q^{3}-\zeta_{24}^{8}q^{4}+\cdots$
1176.1.be.a	$1176$	$1$	1176.be	168.ae	$6$	$16$	$8$	$0.587$	$\Q(\zeta_{48})$	$D_{8}$	$\Q(\sqrt{-2}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{48}^{4}q^{2}+\zeta_{48}^{5}q^{3}+\zeta_{48}^{8}q^{4}+\cdots$
1176.1.bj.a	$1176$	$1$	1176.bj	1176.aj	$14$	$6$	$1$	$0.587$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$-1$	$-1$	$-2$	$-1$		$1$		$q-\zeta_{14}^{3}q^{2}+\zeta_{14}^{2}q^{3}+\zeta_{14}^{6}q^{4}+\cdots$
1176.1.bj.b	$1176$	$1$	1176.bj	1176.aj	$14$	$6$	$1$	$0.587$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$1$	$1$	$2$	$-1$		$1$		$q+\zeta_{14}^{3}q^{2}-\zeta_{14}^{2}q^{3}+\zeta_{14}^{6}q^{4}+\cdots$
1176.1.ck.a	$1176$	$1$	1176.ck	1176.bk	$42$	$12$	$1$	$0.587$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$-1$	$-1$	$1$	$1$		$1$		$q+\zeta_{42}^{13}q^{2}+\zeta_{42}^{11}q^{3}-\zeta_{42}^{5}q^{4}+\cdots$
1176.1.ck.b	$1176$	$1$	1176.ck	1176.bk	$42$	$12$	$1$	$0.587$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$1$	$1$	$-1$	$1$		$1$		$q-\zeta_{42}^{13}q^{2}-\zeta_{42}^{11}q^{3}-\zeta_{42}^{5}q^{4}+\cdots$
1176.2.a.a	$1176$	$2$	1176.a	1.a	$1$	$1$	$1$	$9.390$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{9}+2q^{13}+2q^{15}+\cdots$
1176.2.a.b	$1176$	$2$	1176.a	1.a	$1$	$1$	$1$	$9.390$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}-4q^{13}-4q^{17}+4q^{19}+\cdots$
1176.2.a.c	$1176$	$2$	1176.a	1.a	$1$	$1$	$1$	$9.390$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}+3q^{11}-4q^{13}+\cdots$
1176.2.a.d	$1176$	$2$	1176.a	1.a	$1$	$1$	$1$	$9.390$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+q^{9}-6q^{11}-3q^{13}+\cdots$
1176.2.a.e	$1176$	$2$	1176.a	1.a	$1$	$1$	$1$	$9.390$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{9}-6q^{11}+3q^{13}+\cdots$
1176.2.a.f	$1176$	$2$	1176.a	1.a	$1$	$1$	$1$	$9.390$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{9}-6q^{13}-2q^{15}+\cdots$
1176.2.a.g	$1176$	$2$	1176.a	1.a	$1$	$1$	$1$	$9.390$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}+3q^{11}+4q^{13}+\cdots$
1176.2.a.h	$1176$	$2$	1176.a	1.a	$1$	$1$	$1$	$9.390$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}+4q^{13}+4q^{17}-4q^{19}+\cdots$
1176.2.a.i	$1176$	$2$	1176.a	1.a	$1$	$1$	$1$	$9.390$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots$
1176.2.a.j	$1176$	$2$	1176.a	1.a	$1$	$2$	$2$	$9.390$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-2+\beta )q^{5}+q^{9}+(2-2\beta )q^{11}+\cdots$
1176.2.a.k	$1176$	$2$	1176.a	1.a	$1$	$2$	$2$	$9.390$	$\Q(\sqrt{57}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta q^{5}+q^{9}-\beta q^{11}+(3-\beta )q^{13}+\cdots$
1176.2.a.l	$1176$	$2$	1176.a	1.a	$1$	$2$	$2$	$9.390$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(2+\beta )q^{5}+q^{9}+(-2+2\beta )q^{11}+\cdots$
1176.2.a.m	$1176$	$2$	1176.a	1.a	$1$	$2$	$2$	$9.390$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-2+\beta )q^{5}+q^{9}+(-2-2\beta )q^{11}+\cdots$
1176.2.a.n	$1176$	$2$	1176.a	1.a	$1$	$2$	$2$	$9.390$	$\Q(\sqrt{57}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+q^{9}-\beta q^{11}+(-3+\beta )q^{13}+\cdots$
1176.2.a.o	$1176$	$2$	1176.a	1.a	$1$	$2$	$2$	$9.390$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(2+\beta )q^{5}+q^{9}+(2+2\beta )q^{11}+\cdots$
1176.2.c.a	$1176$	$2$	1176.c	8.b	$2$	$2$	$2$	$9.390$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+i)q^{2}-iq^{3}-2iq^{4}+2iq^{5}+\cdots$
1176.2.c.b	$1176$	$2$	1176.c	8.b	$2$	$4$	$4$	$9.390$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\zeta_{12}^{3})q^{2}+\zeta_{12}^{2}q^{3}+(\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{4}+\cdots$
1176.2.c.c	$1176$	$2$	1176.c	8.b	$2$	$8$	$8$	$9.390$	8.0.386672896.3	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-\beta _{4}q^{3}+\beta _{2}q^{4}+(\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots$
1176.2.c.d	$1176$	$2$	1176.c	8.b	$2$	$12$	$12$	$9.390$	12.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$2$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{2}+\beta _{7}q^{3}-\beta _{11}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
1176.2.c.e	$1176$	$2$	1176.c	8.b	$2$	$16$	$16$	$9.390$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{2}+\beta _{5}q^{3}-\beta _{2}q^{4}-\beta _{4}q^{5}+\cdots$
1176.2.c.f	$1176$	$2$	1176.c	8.b	$2$	$16$	$16$	$9.390$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{10}q^{2}+\beta _{4}q^{3}-\beta _{3}q^{4}-\beta _{2}q^{5}+\cdots$
1176.2.c.g	$1176$	$2$	1176.c	8.b	$2$	$24$	$24$	$9.390$		$_{}$	None	None		$4$	$0$	$4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1176.2.k.a	$1176$	$2$	1176.k	21.c	$2$	$16$	$16$	$9.390$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+\beta _{8}q^{5}+\beta _{5}q^{9}-\beta _{6}q^{11}+\cdots$
1176.2.k.b	$1176$	$2$	1176.k	21.c	$2$	$24$	$24$	$9.390$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1176.2.p.a	$1176$	$2$	1176.p	56.e	$2$	$32$	$32$	$9.390$		$_{}$	None	None		$4$	$0$	$4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1176.2.p.b	$1176$	$2$	1176.p	56.e	$2$	$48$	$48$	$9.390$		$_{}$	None	None		$4$	$0$	$-8$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1176.2.q.a	$1176$	$2$	1176.q	7.c	$3$	$2$	$1$	$9.390$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$
1176.2.q.b	$1176$	$2$	1176.q	7.c	$3$	$2$	$1$	$9.390$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$
1176.2.q.c	$1176$	$2$	1176.q	7.c	$3$	$2$	$1$	$9.390$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{9}+4q^{13}+(-4+\cdots)q^{17}+\cdots$
1176.2.q.d	$1176$	$2$	1176.q	7.c	$3$	$2$	$1$	$9.390$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$
1176.2.q.e	$1176$	$2$	1176.q	7.c	$3$	$2$	$1$	$9.390$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$
1176.2.q.f	$1176$	$2$	1176.q	7.c	$3$	$2$	$1$	$9.390$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+6q^{13}+\cdots$
1176.2.q.g	$1176$	$2$	1176.q	7.c	$3$	$2$	$1$	$9.390$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots$
1176.2.q.h	$1176$	$2$	1176.q	7.c	$3$	$2$	$1$	$9.390$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{9}-4q^{13}+(4-4\zeta_{6})q^{17}+\cdots$
1176.2.q.i	$1176$	$2$	1176.q	7.c	$3$	$2$	$1$	$9.390$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-4+\cdots)q^{11}+\cdots$
1176.2.q.j	$1176$	$2$	1176.q	7.c	$3$	$2$	$1$	$9.390$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+2q^{13}+\cdots$

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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.