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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 52 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
3185.1.o.a	$3185$	$1$	3185.o	65.g	$4$	$4$	$2$	$1.590$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-35}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}+\cdots$
3185.1.q.a	$3185$	$1$	3185.q	65.h	$4$	$4$	$2$	$1.590$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-91}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}-\zeta_{8}^{2}q^{9}-\zeta_{8}^{3}q^{13}+\cdots$
3185.1.y.a	$3185$	$1$	3185.y	455.y	$6$	$2$	$1$	$1.590$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$-1$	$1$	$0$		$1$		$q-\zeta_{6}q^{3}+q^{4}+\zeta_{6}q^{5}-\zeta_{6}q^{11}-\zeta_{6}q^{12}+\cdots$
3185.1.y.b	$3185$	$1$	3185.y	455.y	$6$	$2$	$1$	$1.590$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$1$	$-1$	$0$		$1$		$q+\zeta_{6}q^{3}+q^{4}-\zeta_{6}q^{5}-\zeta_{6}q^{11}+\zeta_{6}q^{12}+\cdots$
3185.1.bf.a	$3185$	$1$	3185.bf	455.af	$6$	$4$	$2$	$1.590$	$\Q(\sqrt{-3}, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-455}) $	None		$4$	$0$	$-1$	$-1$	$-2$	$0$		$1$		$q-\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$
3185.1.bf.b	$3185$	$1$	3185.bf	455.af	$6$	$4$	$2$	$1.590$	$\Q(\sqrt{-3}, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-455}) $	None		$4$	$0$	$-1$	$1$	$2$	$0$		$1$		$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
3185.1.bf.c	$3185$	$1$	3185.bf	455.af	$6$	$4$	$2$	$1.590$	$\Q(\zeta_{12})$	$D_{2}$	$\Q(\sqrt{-35}) $, $\Q(\sqrt{-91}) $	$\Q(\sqrt{65}) $		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{4}q^{4}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{2}q^{9}+\cdots$
3185.1.bf.d	$3185$	$1$	3185.bf	455.af	$6$	$4$	$2$	$1.590$	$\Q(\sqrt{-3}, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-455}) $	None		$4$	$0$	$1$	$-1$	$2$	$0$		$1$		$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots$
3185.1.bf.e	$3185$	$1$	3185.bf	455.af	$6$	$4$	$2$	$1.590$	$\Q(\sqrt{-3}, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-455}) $	None		$4$	$0$	$1$	$1$	$-2$	$0$		$1$		$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
3185.1.bk.a	$3185$	$1$	3185.bk	455.ak	$6$	$4$	$2$	$1.590$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-35}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{12}-\zeta_{12}^{5})q^{3}-\zeta_{12}^{4}q^{4}-\zeta_{12}q^{5}+\cdots$
3185.1.bw.a	$3185$	$1$	3185.bw	455.aw	$6$	$2$	$1$	$1.590$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$-2$	$-1$	$0$		$1$		$q-q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+q^{11}+\zeta_{6}q^{12}+\cdots$
3185.1.bw.b	$3185$	$1$	3185.bw	455.aw	$6$	$2$	$1$	$1.590$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$2$	$1$	$0$		$1$		$q+q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+q^{11}-\zeta_{6}q^{12}+\cdots$
3185.1.bx.a	$3185$	$1$	3185.bx	455.ax	$6$	$4$	$2$	$1.590$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-35}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{12}+\zeta_{12}^{3})q^{3}-q^{4}+\zeta_{12}^{5}q^{5}+\cdots$
3185.1.ck.a	$3185$	$1$	3185.ck	455.bj	$12$	$8$	$2$	$1.590$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-35}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{24}^{5}+\zeta_{24}^{7})q^{3}-\zeta_{24}^{10}q^{4}+\zeta_{24}q^{5}+\cdots$
3185.1.cr.a	$3185$	$1$	3185.cr	455.bq	$12$	$8$	$2$	$1.590$	$\Q(\zeta_{24})$	$S_{4}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{7}q^{3}+\zeta_{24}^{6}q^{4}+\zeta_{24}q^{5}+\zeta_{24}q^{12}+\cdots$
3185.1.cw.a	$3185$	$1$	3185.cw	455.bv	$12$	$8$	$2$	$1.590$	$\Q(\zeta_{24})$	$D_{4}$	$\Q(\sqrt{-91}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{2}q^{4}-\zeta_{24}^{7}q^{5}-\zeta_{24}^{10}q^{9}+\cdots$
3185.1.cy.a	$3185$	$1$	3185.cy	455.bx	$12$	$8$	$2$	$1.590$	$\Q(\zeta_{24})$	$S_{4}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{9}q^{3}+\zeta_{24}^{10}q^{4}+\zeta_{24}^{7}q^{5}+\cdots$
3185.1.cz.a	$3185$	$1$	3185.cz	65.q	$12$	$8$	$2$	$1.590$	$\Q(\zeta_{24})$	$S_{4}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}q^{3}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{3}q^{5}-\zeta_{24}^{3}q^{12}+\cdots$
3185.1.di.a	$3185$	$1$	3185.di	455.ch	$12$	$8$	$2$	$1.590$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-35}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{24}^{3}-\zeta_{24}^{5})q^{3}+\zeta_{24}^{6}q^{4}-\zeta_{24}q^{5}+\cdots$
3185.1.dj.a	$3185$	$1$	3185.dj	455.ci	$12$	$8$	$2$	$1.590$	$\Q(\zeta_{24})$	$D_{4}$	$\Q(\sqrt{-35}) $	None		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{24}-\zeta_{24}^{7})q^{3}+\zeta_{24}^{10}q^{4}-\zeta_{24}^{11}q^{5}+\cdots$
3185.1.dm.a	$3185$	$1$	3185.dm	65.s	$12$	$8$	$2$	$1.590$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-35}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{24}^{7}-\zeta_{24}^{9})q^{3}-\zeta_{24}^{10}q^{4}+\zeta_{24}^{9}q^{5}+\cdots$
3185.2.a.a	$3185$	$2$	3185.a	1.a	$1$	$1$	$1$	$25.432$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-3$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}-q^{4}+q^{5}+3q^{6}+3q^{8}+\cdots$
3185.2.a.b	$3185$	$2$	3185.a	1.a	$1$	$1$	$1$	$25.432$	$\Q$	$_{}$	None	None	✓	$1$	$2$	$-1$	$-2$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}-q^{4}-q^{5}+2q^{6}+3q^{8}+\cdots$
3185.2.a.c	$3185$	$2$	3185.a	1.a	$1$	$1$	$1$	$25.432$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{5}+3q^{8}-3q^{9}+q^{10}+\cdots$
3185.2.a.d	$3185$	$2$	3185.a	1.a	$1$	$1$	$1$	$25.432$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$2$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}-q^{4}+q^{5}-2q^{6}+3q^{8}+\cdots$
3185.2.a.e	$3185$	$2$	3185.a	1.a	$1$	$1$	$1$	$25.432$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$2$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}-q^{4}+q^{5}-2q^{6}+3q^{8}+\cdots$
3185.2.a.f	$3185$	$2$	3185.a	1.a	$1$	$1$	$1$	$25.432$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$3$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}-q^{4}-q^{5}-3q^{6}+3q^{8}+\cdots$
3185.2.a.g	$3185$	$2$	3185.a	1.a	$1$	$1$	$1$	$25.432$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$-3$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}-q^{4}-q^{5}-3q^{6}-3q^{8}+\cdots$
3185.2.a.h	$3185$	$2$	3185.a	1.a	$1$	$1$	$1$	$25.432$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{5}-3q^{8}-3q^{9}+q^{10}+\cdots$
3185.2.a.i	$3185$	$2$	3185.a	1.a	$1$	$1$	$1$	$25.432$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$1$	$3$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}-q^{4}+q^{5}+3q^{6}-3q^{8}+\cdots$
3185.2.a.j	$3185$	$2$	3185.a	1.a	$1$	$2$	$2$	$25.432$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-\beta q^{3}+(1-2\beta )q^{4}+\cdots$
3185.2.a.k	$3185$	$2$	3185.a	1.a	$1$	$2$	$2$	$25.432$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(-1+\beta )q^{3}+q^{4}+q^{5}+(3+\cdots)q^{6}+\cdots$
3185.2.a.l	$3185$	$2$	3185.a	1.a	$1$	$4$	$4$	$25.432$	4.4.12197.1	$_{}$	None	None	✓	$1$	$1$	$-1$	$0$	$4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2}-\beta _{3})q^{4}+\cdots$
3185.2.a.m	$3185$	$2$	3185.a	1.a	$1$	$4$	$4$	$25.432$	4.4.725.1	$_{}$	None	None	✓	$1$	$1$	$1$	$-3$	$4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}-\beta _{2})q^{2}+(-1-\beta _{1}+\beta _{3})q^{3}+\cdots$
3185.2.a.n	$3185$	$2$	3185.a	1.a	$1$	$4$	$4$	$25.432$	4.4.725.1	$_{}$	None	None	✓	$1$	$1$	$1$	$-2$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1+\beta _{3})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots$
3185.2.a.o	$3185$	$2$	3185.a	1.a	$1$	$4$	$4$	$25.432$	4.4.725.1	$_{}$	None	None	✓	$1$	$1$	$1$	$2$	$4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
3185.2.a.p	$3185$	$2$	3185.a	1.a	$1$	$4$	$4$	$25.432$	4.4.725.1	$_{}$	None	None	✓	$1$	$0$	$1$	$3$	$-4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1}-\beta _{2})q^{2}+(1+\beta _{1}-\beta _{3})q^{3}+\cdots$
3185.2.a.q	$3185$	$2$	3185.a	1.a	$1$	$4$	$4$	$25.432$	4.4.1957.1	$_{}$	None	None	✓	$1$	$1$	$3$	$-4$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1}+\beta _{2})q^{2}+(-1+\beta _{2}+\beta _{3})q^{3}+\cdots$
3185.2.a.r	$3185$	$2$	3185.a	1.a	$1$	$6$	$6$	$25.432$	6.6.45853772.1	$_{}$	None	None	✓	$1$	$0$	$3$	$0$	$-6$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{5}q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+\cdots$
3185.2.a.s	$3185$	$2$	3185.a	1.a	$1$	$7$	$7$	$25.432$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-2$	$-1$	$-7$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{2}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
3185.2.a.t	$3185$	$2$	3185.a	1.a	$1$	$7$	$7$	$25.432$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-2$	$1$	$7$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{2}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
3185.2.a.u	$3185$	$2$	3185.a	1.a	$1$	$7$	$7$	$25.432$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$7$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{6}q^{3}+(2+\beta _{1}+\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$
3185.2.a.v	$3185$	$2$	3185.a	1.a	$1$	$8$	$8$	$25.432$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-2$	$-4$	$8$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
3185.2.a.w	$3185$	$2$	3185.a	1.a	$1$	$8$	$8$	$25.432$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-2$	$4$	$-8$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{5})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots$
3185.2.a.x	$3185$	$2$	3185.a	1.a	$1$	$8$	$8$	$25.432$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-4$	$8$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
3185.2.a.y	$3185$	$2$	3185.a	1.a	$1$	$8$	$8$	$25.432$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-1$	$4$	$-8$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
3185.2.a.z	$3185$	$2$	3185.a	1.a	$1$	$8$	$8$	$25.432$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$-2$	$-8$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
3185.2.a.ba	$3185$	$2$	3185.a	1.a	$1$	$8$	$8$	$25.432$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$3$	$2$	$8$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
3185.2.a.bb	$3185$	$2$	3185.a	1.a	$1$	$10$	$10$	$25.432$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-4$	$-10$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
3185.2.a.bc	$3185$	$2$	3185.a	1.a	$1$	$10$	$10$	$25.432$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-1$	$4$	$10$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$

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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.