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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 158 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
330.2.a.a	$330$	$2$	330.a	1.a	$1$	$1$	$1$	$2.635$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots$
330.2.a.b	$330$	$2$	330.a	1.a	$1$	$1$	$1$	$2.635$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-4q^{7}+\cdots$
330.2.a.c	$330$	$2$	330.a	1.a	$1$	$1$	$1$	$2.635$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+4q^{7}+\cdots$
330.2.a.d	$330$	$2$	330.a	1.a	$1$	$1$	$1$	$2.635$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
330.2.a.e	$330$	$2$	330.a	1.a	$1$	$1$	$1$	$2.635$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{8}+\cdots$
330.2.c.a	$330$	$2$	330.c	5.b	$2$	$4$	$4$	$2.635$	$\Q(i, \sqrt{10})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+\beta _{2}q^{3}-q^{4}+\beta _{1}q^{5}-q^{6}+\cdots$
330.2.c.b	$330$	$2$	330.c	5.b	$2$	$4$	$4$	$2.635$	$\Q(\zeta_{8})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}^{2}q^{2}-\zeta_{8}^{2}q^{3}-q^{4}+(2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots$
330.2.d.a	$330$	$2$	330.d	33.d	$2$	$8$	$8$	$2.635$	8.0.2051727616.3	None		$2$	$0$	$-8$	$2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+(\beta _{3}+\beta _{4})q^{3}+q^{4}-\beta _{4}q^{5}+\cdots$
330.2.d.b	$330$	$2$	330.d	33.d	$2$	$8$	$8$	$2.635$	8.0.2051727616.3	None		$2$	$0$	$8$	$2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+(\beta _{3}+\beta _{4})q^{3}+q^{4}-\beta _{4}q^{5}+\cdots$
330.2.f.a	$330$	$2$	330.f	165.d	$2$	$24$	$24$	$2.635$		None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
330.2.j.a	$330$	$2$	330.j	15.e	$4$	$20$	$10$	$2.635$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{6}q^{2}-\beta _{3}q^{3}-\beta _{14}q^{4}+(\beta _{6}-\beta _{7}+\cdots)q^{5}+\cdots$
330.2.j.b	$330$	$2$	330.j	15.e	$4$	$20$	$10$	$2.635$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$0$	$4$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{6}q^{2}+\beta _{1}q^{3}-\beta _{14}q^{4}+(-\beta _{6}+\cdots)q^{5}+\cdots$
330.2.l.a	$330$	$2$	330.l	55.e	$4$	$4$	$2$	$2.635$	$\Q(\zeta_{8})$	None		$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+(2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots$
330.2.l.b	$330$	$2$	330.l	55.e	$4$	$4$	$2$	$2.635$	$\Q(\zeta_{8})$	None		$2$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+(-2\zeta_{8}+\cdots)q^{5}+\cdots$
330.2.l.c	$330$	$2$	330.l	55.e	$4$	$8$	$4$	$2.635$	8.0.822083584.4	None		$2$	$0$	$0$	$0$	$-8$	$-8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{2}-\beta _{2}q^{3}+\beta _{4}q^{4}+(-1+\beta _{6}+\cdots)q^{5}+\cdots$
330.2.l.d	$330$	$2$	330.l	55.e	$4$	$8$	$4$	$2.635$	8.0.822083584.4	None		$2$	$0$	$0$	$0$	$-8$	$8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{6}q^{2}+\beta _{6}q^{3}-\beta _{4}q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots$
330.2.m.a	$330$	$2$	330.m	11.c	$5$	$4$	$1$	$2.635$	$\Q(\zeta_{10})$	None		$2$	$0$	$-1$	$1$	$-1$	$5$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
330.2.m.b	$330$	$2$	330.m	11.c	$5$	$4$	$1$	$2.635$	$\Q(\zeta_{10})$	None		$2$	$0$	$-1$	$1$	$1$	$-4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
330.2.m.c	$330$	$2$	330.m	11.c	$5$	$4$	$1$	$2.635$	$\Q(\zeta_{10})$	None		$2$	$0$	$1$	$1$	$-1$	$4$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots$
330.2.m.d	$330$	$2$	330.m	11.c	$5$	$4$	$1$	$2.635$	$\Q(\zeta_{10})$	None		$2$	$0$	$1$	$1$	$1$	$-5$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots$
330.2.m.e	$330$	$2$	330.m	11.c	$5$	$8$	$2$	$2.635$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$-2$	$-2$	$-2$	$-3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{2}q^{2}+\beta _{4}q^{3}-\beta _{3}q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots$
330.2.m.f	$330$	$2$	330.m	11.c	$5$	$8$	$2$	$2.635$	8.0.2769390625.1	None		$2$	$0$	$2$	$-2$	$2$	$3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{5}q^{2}+(-1-\beta _{2}+\beta _{3}-\beta _{5})q^{3}+\cdots$
330.2.p.a	$330$	$2$	330.p	165.r	$10$	$96$	$24$	$2.635$		None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
330.2.r.a	$330$	$2$	330.r	33.f	$10$	$32$	$8$	$2.635$		None		$2$	$0$	$-8$	$-2$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
330.2.r.b	$330$	$2$	330.r	33.f	$10$	$32$	$8$	$2.635$		None		$2$	$0$	$8$	$-2$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
330.2.s.a	$330$	$2$	330.s	55.j	$10$	$8$	$2$	$2.635$	$\Q(\zeta_{20})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\zeta_{20}q^{2}-\zeta_{20}^{3}q^{3}+\zeta_{20}^{2}q^{4}+(\zeta_{20}+\cdots)q^{5}+\cdots$
330.2.s.b	$330$	$2$	330.s	55.j	$10$	$8$	$2$	$2.635$	$\Q(\zeta_{20})$	None		$4$	$0$	$0$	$0$	$10$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\zeta_{20}q^{2}-\zeta_{20}^{3}q^{3}+\zeta_{20}^{2}q^{4}+(2\zeta_{20}^{2}+\cdots)q^{5}+\cdots$
330.2.s.c	$330$	$2$	330.s	55.j	$10$	$32$	$8$	$2.635$		None		$4$	$0$	$0$	$0$	$-2$	$0$			$\mathrm{SU}(2)[C_{10}]$
330.2.u.a	$330$	$2$	330.u	55.l	$20$	$48$	$6$	$2.635$		None		$2$	$0$	$0$	$0$	$8$	$16$			$\mathrm{SU}(2)[C_{20}]$
330.2.u.b	$330$	$2$	330.u	55.l	$20$	$48$	$6$	$2.635$		None		$2$	$0$	$0$	$0$	$8$	$24$			$\mathrm{SU}(2)[C_{20}]$
330.2.w.a	$330$	$2$	330.w	165.v	$20$	$192$	$24$	$2.635$		None		$8$	$0$	$0$	$4$	$0$	$8$			$\mathrm{SU}(2)[C_{20}]$
330.3.b.a	$330$	$3$	330.b	11.b	$2$	$16$	$16$	$8.992$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+\beta _{6}q^{3}-2q^{4}-\beta _{5}q^{5}+\beta _{13}q^{6}+\cdots$
330.3.e.a	$330$	$3$	330.e	15.d	$2$	$40$	$40$	$8.992$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
330.3.g.a	$330$	$3$	330.g	3.b	$2$	$24$	$24$	$8.992$		None		$2$	$0$	$0$	$0$	$0$	$-16$			$\mathrm{SU}(2)[C_{2}]$
330.3.h.a	$330$	$3$	330.h	55.d	$2$	$24$	$24$	$8.992$		None		$4$	$0$	$0$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{2}]$
330.3.i.a	$330$	$3$	330.i	5.c	$4$	$16$	$8$	$8.992$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$16$	$0$	$0$	$0$		$2^{12}\cdot 5$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{6})q^{2}+\beta _{5}q^{3}+2\beta _{6}q^{4}+(-\beta _{11}+\cdots)q^{5}+\cdots$
330.3.i.b	$330$	$3$	330.i	5.c	$4$	$24$	$12$	$8.992$		None		$2$	$0$	$-24$	$0$	$-16$	$0$			$\mathrm{SU}(2)[C_{4}]$
330.3.k.a	$330$	$3$	330.k	165.l	$4$	$48$	$24$	$8.992$		None		$4$	$0$	$-48$	$2$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
330.3.k.b	$330$	$3$	330.k	165.l	$4$	$48$	$24$	$8.992$		None		$4$	$0$	$48$	$2$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
330.3.n.a	$330$	$3$	330.n	55.h	$10$	$96$	$24$	$8.992$		None		$4$	$0$	$0$	$0$	$8$	$0$			$\mathrm{SU}(2)[C_{10}]$
330.3.o.a	$330$	$3$	330.o	33.h	$10$	$128$	$32$	$8.992$		None		$4$	$0$	$0$	$-8$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
330.3.q.a	$330$	$3$	330.q	165.o	$10$	$192$	$48$	$8.992$		None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
330.3.t.a	$330$	$3$	330.t	11.d	$10$	$32$	$8$	$8.992$		None		$2$	$0$	$0$	$0$	$-40$	$20$			$\mathrm{SU}(2)[C_{10}]$
330.3.t.b	$330$	$3$	330.t	11.d	$10$	$32$	$8$	$8.992$		None		$2$	$0$	$0$	$0$	$40$	$-20$			$\mathrm{SU}(2)[C_{10}]$
330.3.v.a	$330$	$3$	330.v	165.u	$20$	$192$	$24$	$8.992$		None		$4$	$0$	$-48$	$-2$	$0$	$0$			$\mathrm{SU}(2)[C_{20}]$
330.3.v.b	$330$	$3$	330.v	165.u	$20$	$192$	$24$	$8.992$		None		$4$	$0$	$48$	$-2$	$0$	$0$			$\mathrm{SU}(2)[C_{20}]$
330.3.x.a	$330$	$3$	330.x	55.k	$20$	$96$	$12$	$8.992$		None		$4$	$0$	$-24$	$0$	$0$	$-68$			$\mathrm{SU}(2)[C_{20}]$
330.3.x.b	$330$	$3$	330.x	55.k	$20$	$96$	$12$	$8.992$		None		$4$	$0$	$24$	$0$	$16$	$-20$			$\mathrm{SU}(2)[C_{20}]$
330.4.a.a	$330$	$4$	330.a	1.a	$1$	$1$	$1$	$19.471$	$\Q$	None	✓	$1$	$1$	$-2$	$-3$	$-5$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots$
330.4.a.b	$330$	$4$	330.a	1.a	$1$	$1$	$1$	$19.471$	$\Q$	None	✓	$1$	$0$	$-2$	$-3$	$5$	$20$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}+5q^{5}+6q^{6}+\cdots$

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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.