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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 118 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
1560.1.y.a	$1560$	$1$	1560.y	1560.y	$2$	$1$	$1$	$0.779$	$\Q$	$D_{2}$	$\Q(\sqrt{-39}) $, $\Q(\sqrt{-390}) $	$\Q(\sqrt{10}) $	✓	$4$	$0$	$-1$	$-1$	$1$	$0$		$1$		$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots$
1560.1.y.b	$1560$	$1$	1560.y	1560.y	$2$	$1$	$1$	$0.779$	$\Q$	$D_{2}$	$\Q(\sqrt{-39}) $, $\Q(\sqrt{-390}) $	$\Q(\sqrt{10}) $	✓	$4$	$0$	$-1$	$1$	$1$	$0$		$1$		$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots$
1560.1.y.c	$1560$	$1$	1560.y	1560.y	$2$	$1$	$1$	$0.779$	$\Q$	$D_{2}$	$\Q(\sqrt{-39}) $, $\Q(\sqrt{-390}) $	$\Q(\sqrt{10}) $	✓	$4$	$0$	$1$	$-1$	$-1$	$0$		$1$		$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots$
1560.1.y.d	$1560$	$1$	1560.y	1560.y	$2$	$1$	$1$	$0.779$	$\Q$	$D_{2}$	$\Q(\sqrt{-39}) $, $\Q(\sqrt{-390}) $	$\Q(\sqrt{10}) $	✓	$4$	$0$	$1$	$1$	$-1$	$0$		$1$		$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
1560.1.y.e	$1560$	$1$	1560.y	1560.y	$2$	$2$	$2$	$0.779$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-39}) $, $\Q(\sqrt{-30}) $	$\Q(\sqrt{130}) $		$8$	$0$	$0$	$-2$	$0$	$0$		$1$		$q-iq^{2}-q^{3}-q^{4}-iq^{5}+iq^{6}+iq^{8}+\cdots$
1560.1.y.f	$1560$	$1$	1560.y	1560.y	$2$	$2$	$2$	$0.779$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-39}) $, $\Q(\sqrt{-30}) $	$\Q(\sqrt{130}) $		$8$	$0$	$0$	$2$	$0$	$0$		$1$		$q-iq^{2}+q^{3}-q^{4}+iq^{5}-iq^{6}+iq^{8}+\cdots$
1560.1.cs.a	$1560$	$1$	1560.cs	1560.bs	$4$	$4$	$2$	$0.779$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-26}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\cdots$
1560.1.cs.b	$1560$	$1$	1560.cs	1560.bs	$4$	$4$	$2$	$0.779$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-26}) $	None		$8$	$0$	$0$	$4$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\cdots$
1560.1.cs.c	$1560$	$1$	1560.cs	1560.bs	$4$	$8$	$4$	$0.779$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-26}) $	None		$8$	$0$	$0$	$-4$	$0$	$0$		$1$		$q+\zeta_{24}^{9}q^{2}+\zeta_{24}^{8}q^{3}-\zeta_{24}^{6}q^{4}+\cdots$
1560.1.cs.d	$1560$	$1$	1560.cs	1560.bs	$4$	$8$	$4$	$0.779$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{3}-\zeta_{16}^{2}q^{4}+\cdots$
1560.1.cs.e	$1560$	$1$	1560.cs	1560.bs	$4$	$8$	$4$	$0.779$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}^{3}q^{2}+\zeta_{16}^{2}q^{3}+\zeta_{16}^{6}q^{4}+\cdots$
1560.1.cs.f	$1560$	$1$	1560.cs	1560.bs	$4$	$8$	$4$	$0.779$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-26}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{9}q^{2}+\zeta_{24}^{2}q^{3}-\zeta_{24}^{6}q^{4}+\cdots$
1560.1.dk.a	$1560$	$1$	1560.dk	1560.ck	$6$	$4$	$2$	$0.779$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-30}) $	None		$8$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+\zeta_{12}q^{2}+\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}+\cdots$
1560.1.dk.b	$1560$	$1$	1560.dk	1560.ck	$6$	$4$	$2$	$0.779$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-30}) $	None		$8$	$0$	$0$	$2$	$0$	$0$		$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}+\cdots$
1560.1.du.a	$1560$	$1$	1560.du	1560.cu	$6$	$2$	$1$	$0.779$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-30}) $	None		$4$	$0$	$-1$	$-1$	$2$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+q^{5}+\cdots$
1560.1.du.b	$1560$	$1$	1560.du	1560.cu	$6$	$2$	$1$	$0.779$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-30}) $	None		$4$	$0$	$-1$	$1$	$-2$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-q^{5}+\cdots$
1560.1.du.c	$1560$	$1$	1560.du	1560.cu	$6$	$2$	$1$	$0.779$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-30}) $	None		$4$	$0$	$1$	$-1$	$-2$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-q^{5}+\cdots$
1560.1.du.d	$1560$	$1$	1560.du	1560.cu	$6$	$2$	$1$	$0.779$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-30}) $	None		$4$	$0$	$1$	$1$	$2$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+q^{5}+\cdots$
1560.2.a.a	$1560$	$2$	1560.a	1.a	$1$	$1$	$1$	$12.457$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}+q^{13}+q^{15}-6q^{17}+\cdots$
1560.2.a.b	$1560$	$2$	1560.a	1.a	$1$	$1$	$1$	$12.457$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+q^{9}+4q^{11}+q^{13}+q^{15}+\cdots$
1560.2.a.c	$1560$	$2$	1560.a	1.a	$1$	$1$	$1$	$12.457$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$1$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-5q^{7}+q^{9}+q^{11}+q^{13}+\cdots$
1560.2.a.d	$1560$	$2$	1560.a	1.a	$1$	$1$	$1$	$12.457$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+q^{9}-4q^{11}+q^{13}-q^{15}+\cdots$
1560.2.a.e	$1560$	$2$	1560.a	1.a	$1$	$1$	$1$	$12.457$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+2q^{7}+q^{9}+4q^{11}-q^{13}+\cdots$
1560.2.a.f	$1560$	$2$	1560.a	1.a	$1$	$1$	$1$	$12.457$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}+4q^{7}+q^{9}+4q^{11}+q^{13}+\cdots$
1560.2.a.g	$1560$	$2$	1560.a	1.a	$1$	$1$	$1$	$12.457$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-4q^{7}+q^{9}+4q^{11}+q^{13}+\cdots$
1560.2.a.h	$1560$	$2$	1560.a	1.a	$1$	$1$	$1$	$12.457$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-q^{7}+q^{9}-5q^{11}+q^{13}+\cdots$
1560.2.a.i	$1560$	$2$	1560.a	1.a	$1$	$1$	$1$	$12.457$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+q^{9}-q^{13}-q^{15}+2q^{17}+\cdots$
1560.2.a.j	$1560$	$2$	1560.a	1.a	$1$	$1$	$1$	$12.457$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-3q^{7}+q^{9}-3q^{11}-q^{13}+\cdots$
1560.2.a.k	$1560$	$2$	1560.a	1.a	$1$	$1$	$1$	$12.457$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}-2q^{7}+q^{9}+q^{13}+q^{15}+\cdots$
1560.2.a.l	$1560$	$2$	1560.a	1.a	$1$	$1$	$1$	$12.457$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+4q^{7}+q^{9}+q^{13}+q^{15}+\cdots$
1560.2.a.m	$1560$	$2$	1560.a	1.a	$1$	$2$	$2$	$12.457$	$\Q(\sqrt{41}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-\beta q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots$
1560.2.a.n	$1560$	$2$	1560.a	1.a	$1$	$2$	$2$	$12.457$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}+\beta q^{7}+q^{9}-\beta q^{11}-q^{13}+\cdots$
1560.2.a.o	$1560$	$2$	1560.a	1.a	$1$	$2$	$2$	$12.457$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{5}-\beta q^{7}+q^{9}+(-4+\beta )q^{11}+\cdots$
1560.2.a.p	$1560$	$2$	1560.a	1.a	$1$	$3$	$3$	$12.457$	3.3.1849.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$-3$	$5$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+(2-\beta _{1})q^{7}+q^{9}+(1+\beta _{2})q^{11}+\cdots$
1560.2.a.q	$1560$	$2$	1560.a	1.a	$1$	$3$	$3$	$12.457$	3.3.940.1	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$3$	$1$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+\beta _{2}q^{7}+q^{9}+(2+\beta _{1}+\cdots)q^{11}+\cdots$
1560.2.g.a	$1560$	$2$	1560.g	13.b	$2$	$2$	$2$	$12.457$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$1$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+iq^{5}+2iq^{7}+q^{9}+(-3+2i)q^{13}+\cdots$
1560.2.g.b	$1560$	$2$	1560.g	13.b	$2$	$2$	$2$	$12.457$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-iq^{5}+2iq^{7}+q^{9}-4iq^{11}+\cdots$
1560.2.g.c	$1560$	$2$	1560.g	13.b	$2$	$2$	$2$	$12.457$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-iq^{5}+4iq^{7}+q^{9}+4iq^{11}+\cdots$
1560.2.g.d	$1560$	$2$	1560.g	13.b	$2$	$2$	$2$	$12.457$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}-iq^{5}+3iq^{7}+q^{9}-3iq^{11}+\cdots$
1560.2.g.e	$1560$	$2$	1560.g	13.b	$2$	$2$	$2$	$12.457$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}-iq^{5}+q^{9}+6iq^{11}+(-2+\cdots)q^{13}+\cdots$
1560.2.g.f	$1560$	$2$	1560.g	13.b	$2$	$4$	$4$	$12.457$	$\Q(i, \sqrt{41})$	$_{}$	None	None		$2$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots$
1560.2.g.g	$1560$	$2$	1560.g	13.b	$2$	$4$	$4$	$12.457$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$4$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}-\zeta_{12}q^{5}+\zeta_{12}^{2}q^{7}+q^{9}+(1+\cdots)q^{13}+\cdots$
1560.2.g.h	$1560$	$2$	1560.g	13.b	$2$	$4$	$4$	$12.457$	$\Q(i, \sqrt{17})$	$_{}$	None	None		$2$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}-\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots$
1560.2.g.i	$1560$	$2$	1560.g	13.b	$2$	$6$	$6$	$12.457$	6.0.3356224.1	$_{}$	None	None		$2$	$0$	$0$	$-6$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-\beta _{1}q^{5}+(-2\beta _{1}+\beta _{4})q^{7}+q^{9}+\cdots$
1560.2.l.a	$1560$	$2$	1560.l	5.b	$2$	$2$	$2$	$12.457$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+(-1+2i)q^{5}+5iq^{7}-q^{9}+\cdots$
1560.2.l.b	$1560$	$2$	1560.l	5.b	$2$	$2$	$2$	$12.457$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{3}+(1+2i)q^{5}+iq^{7}-q^{9}+3q^{11}+\cdots$
1560.2.l.c	$1560$	$2$	1560.l	5.b	$2$	$6$	$6$	$12.457$	6.0.5161984.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}-\beta _{5}q^{5}-q^{9}+(-2+\beta _{4}+\cdots)q^{11}+\cdots$
1560.2.l.d	$1560$	$2$	1560.l	5.b	$2$	$8$	$8$	$12.457$	8.0.$\cdots$.2	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}-\beta _{7}q^{5}+(-\beta _{1}+2\beta _{2})q^{7}+\cdots$
1560.2.l.e	$1560$	$2$	1560.l	5.b	$2$	$8$	$8$	$12.457$	8.0.1698758656.6	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{3}+(-\beta _{2}-\beta _{3})q^{5}-\beta _{4}q^{7}+\cdots$
1560.2.l.f	$1560$	$2$	1560.l	5.b	$2$	$10$	$10$	$12.457$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{3}+\beta _{2}q^{5}-\beta _{9}q^{7}-q^{9}+(1+\cdots)q^{11}+\cdots$

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