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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 107 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
1960.1.i.a	$1960$	$1$	1960.i	40.e	$2$	$1$	$1$	$0.978$	$\Q$	$D_{3}$	$\Q(\sqrt{-10}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$0$		$1$		$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{9}+q^{10}+\cdots$
1960.1.i.b	$1960$	$1$	1960.i	40.e	$2$	$1$	$1$	$0.978$	$\Q$	$D_{3}$	$\Q(\sqrt{-10}) $	None	✓	$2$	$0$	$-1$	$0$	$1$	$0$		$1$		$q-q^{2}+q^{4}+q^{5}-q^{8}+q^{9}-q^{10}+\cdots$
1960.1.i.c	$1960$	$1$	1960.i	40.e	$2$	$1$	$1$	$0.978$	$\Q$	$D_{3}$	$\Q(\sqrt{-10}) $	None	✓	$2$	$0$	$1$	$0$	$-1$	$0$		$1$		$q+q^{2}+q^{4}-q^{5}+q^{8}+q^{9}-q^{10}+\cdots$
1960.1.i.d	$1960$	$1$	1960.i	40.e	$2$	$1$	$1$	$0.978$	$\Q$	$D_{3}$	$\Q(\sqrt{-10}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$0$		$1$		$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{9}+q^{10}+\cdots$
1960.1.u.a	$1960$	$1$	1960.u	40.i	$4$	$8$	$4$	$0.978$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{2}q^{2}+(\zeta_{16}^{5}-\zeta_{16}^{7})q^{3}+\zeta_{16}^{4}q^{4}+\cdots$
1960.1.v.a	$1960$	$1$	1960.v	5.c	$4$	$4$	$2$	$0.978$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{3}-\zeta_{8}q^{5}+q^{11}+\zeta_{8}q^{13}+\cdots$
1960.1.bi.a	$1960$	$1$	1960.bi	280.ai	$6$	$2$	$1$	$0.978$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$-1$	$0$	$1$	$0$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+q^{8}-\zeta_{6}q^{9}+\cdots$
1960.1.bi.b	$1960$	$1$	1960.bi	280.ai	$6$	$2$	$1$	$0.978$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$1$	$0$	$-1$	$0$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}-q^{8}-\zeta_{6}q^{9}+\cdots$
1960.1.bk.a	$1960$	$1$	1960.bk	280.ak	$6$	$8$	$4$	$0.978$	$\Q(\zeta_{24})$	$D_{4}$	$\Q(\sqrt{-14}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{2}q^{2}+(-\zeta_{24}+\zeta_{24}^{7})q^{3}+\zeta_{24}^{4}q^{4}+\cdots$
1960.1.br.a	$1960$	$1$	1960.br	35.l	$12$	$8$	$2$	$0.978$	$\Q(\zeta_{24})$	$S_{4}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{24}^{7}q^{3}-\zeta_{24}^{11}q^{5}-\zeta_{24}^{4}q^{11}+\cdots$
1960.1.bu.a	$1960$	$1$	1960.bu	280.at	$12$	$16$	$4$	$0.978$	$\Q(\zeta_{48})$	$D_{8}$	$\Q(\sqrt{-14}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{48}^{2}q^{2}+(-\zeta_{48}-\zeta_{48}^{19})q^{3}+\cdots$
1960.1.cf.a	$1960$	$1$	1960.cf	1960.bf	$14$	$6$	$1$	$0.978$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$-1$	$0$	$-1$	$-1$		$1$		$q-\zeta_{14}^{5}q^{2}-\zeta_{14}^{3}q^{4}-\zeta_{14}q^{5}+\zeta_{14}^{6}q^{7}+\cdots$
1960.1.cf.b	$1960$	$1$	1960.cf	1960.bf	$14$	$6$	$1$	$0.978$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$1$	$0$	$1$	$1$		$1$		$q+\zeta_{14}^{5}q^{2}-\zeta_{14}^{3}q^{4}+\zeta_{14}q^{5}-\zeta_{14}^{6}q^{7}+\cdots$
1960.1.cz.a	$1960$	$1$	1960.cz	1960.bz	$42$	$12$	$1$	$0.978$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$-1$	$0$	$-1$	$2$		$1$		$q-\zeta_{42}^{16}q^{2}-\zeta_{42}^{11}q^{4}+\zeta_{42}^{13}q^{5}+\cdots$
1960.1.cz.b	$1960$	$1$	1960.cz	1960.bz	$42$	$12$	$1$	$0.978$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$1$	$0$	$1$	$-2$		$1$		$q+\zeta_{42}^{16}q^{2}-\zeta_{42}^{11}q^{4}-\zeta_{42}^{13}q^{5}+\cdots$
1960.2.a.a	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+q^{9}-q^{11}-3q^{13}+\cdots$
1960.2.a.b	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots$
1960.2.a.c	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-2q^{9}-2q^{11}+4q^{13}+\cdots$
1960.2.a.d	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{9}-5q^{11}-7q^{13}+\cdots$
1960.2.a.e	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{9}+2q^{11}-q^{15}+\cdots$
1960.2.a.f	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-2q^{9}+3q^{11}+q^{13}+\cdots$
1960.2.a.g	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{9}+4q^{11}+2q^{13}-2q^{17}+\cdots$
1960.2.a.h	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{9}-5q^{11}+7q^{13}+\cdots$
1960.2.a.i	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{9}+2q^{11}-q^{15}+\cdots$
1960.2.a.j	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-2q^{9}+3q^{11}-q^{13}+\cdots$
1960.2.a.k	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{9}-5q^{11}-q^{13}+\cdots$
1960.2.a.l	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{9}-2q^{11}-4q^{13}+\cdots$
1960.2.a.m	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+q^{9}-q^{11}+3q^{13}+\cdots$
1960.2.a.n	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots$
1960.2.a.o	$1960$	$2$	1960.a	1.a	$1$	$1$	$1$	$15.651$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-q^{5}+6q^{9}-5q^{11}+5q^{13}+\cdots$
1960.2.a.p	$1960$	$2$	1960.a	1.a	$1$	$2$	$2$	$15.651$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+q^{5}-2\beta q^{9}+(-2+\cdots)q^{11}+\cdots$
1960.2.a.q	$1960$	$2$	1960.a	1.a	$1$	$2$	$2$	$15.651$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+q^{5}-2\beta q^{9}-q^{11}+\cdots$
1960.2.a.r	$1960$	$2$	1960.a	1.a	$1$	$2$	$2$	$15.651$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}-q^{5}+(1+\beta )q^{9}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
1960.2.a.s	$1960$	$2$	1960.a	1.a	$1$	$2$	$2$	$15.651$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+q^{5}+(5+\beta )q^{9}+(4-\beta )q^{11}+\cdots$
1960.2.a.t	$1960$	$2$	1960.a	1.a	$1$	$2$	$2$	$15.651$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-q^{5}+2\beta q^{9}+(-2-2\beta )q^{11}+\cdots$
1960.2.a.u	$1960$	$2$	1960.a	1.a	$1$	$2$	$2$	$15.651$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-q^{5}+2\beta q^{9}-q^{11}+(1+\cdots)q^{13}+\cdots$
1960.2.a.v	$1960$	$2$	1960.a	1.a	$1$	$3$	$3$	$15.651$	3.3.1944.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}-q^{5}+(3+\beta _{1}+\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots$
1960.2.a.w	$1960$	$2$	1960.a	1.a	$1$	$3$	$3$	$15.651$	3.3.1944.1	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}+q^{5}+(3+\beta _{1}+\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots$
1960.2.a.x	$1960$	$2$	1960.a	1.a	$1$	$4$	$4$	$15.651$	4.4.16448.2	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{3}-q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$
1960.2.a.y	$1960$	$2$	1960.a	1.a	$1$	$4$	$4$	$15.651$	4.4.16448.2	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{3}+q^{5}+(1+\beta _{1}+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$
1960.2.g.a	$1960$	$2$	1960.g	5.b	$2$	$2$	$2$	$15.651$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+(-2-i)q^{5}+2q^{9}-q^{11}+\cdots$
1960.2.g.b	$1960$	$2$	1960.g	5.b	$2$	$2$	$2$	$15.651$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+(1-i)q^{5}-q^{9}-4q^{11}+2iq^{13}+\cdots$
1960.2.g.c	$1960$	$2$	1960.g	5.b	$2$	$6$	$6$	$15.651$	6.0.5161984.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{3}+(-\beta _{2}-\beta _{5})q^{5}+(-1-\beta _{1}+\cdots)q^{9}+\cdots$
1960.2.g.d	$1960$	$2$	1960.g	5.b	$2$	$8$	$8$	$15.651$	8.0.$\cdots$.3	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{3}-\beta _{6}q^{5}-\beta _{2}q^{9}+(1+\beta _{2}+\cdots)q^{11}+\cdots$
1960.2.g.e	$1960$	$2$	1960.g	5.b	$2$	$12$	$12$	$15.651$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{4}q^{5}+(-1+\beta _{2})q^{9}+\beta _{3}q^{11}+\cdots$
1960.2.g.f	$1960$	$2$	1960.g	5.b	$2$	$12$	$12$	$15.651$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{5}q^{5}+(-1+\beta _{2})q^{9}+\beta _{3}q^{11}+\cdots$
1960.2.g.g	$1960$	$2$	1960.g	5.b	$2$	$20$	$20$	$15.651$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{25}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{17}q^{3}-\beta _{16}q^{5}+(-1+\beta _{1})q^{9}+\cdots$
1960.2.q.a	$1960$	$2$	1960.q	7.c	$3$	$2$	$1$	$15.651$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-3$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-3+3\zeta_{6})q^{3}+\zeta_{6}q^{5}-6\zeta_{6}q^{9}+\cdots$
1960.2.q.b	$1960$	$2$	1960.q	7.c	$3$	$2$	$1$	$15.651$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$
1960.2.q.c	$1960$	$2$	1960.q	7.c	$3$	$2$	$1$	$15.651$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$

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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.