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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 54 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
3864.1.v.a	$3864$	$1$	3864.v	3864.v	$2$	$1$	$1$	$1.928$	$\Q$	$D_{3}$	$\Q(\sqrt{-966}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$-1$		$1$		$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
3864.1.v.b	$3864$	$1$	3864.v	3864.v	$2$	$1$	$1$	$1.928$	$\Q$	$D_{3}$	$\Q(\sqrt{-966}) $	None	✓	$2$	$0$	$-1$	$-1$	$1$	$1$		$1$		$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
3864.1.v.c	$3864$	$1$	3864.v	3864.v	$2$	$1$	$1$	$1.928$	$\Q$	$D_{3}$	$\Q(\sqrt{-966}) $	None	✓	$2$	$0$	$-1$	$1$	$-1$	$-1$		$1$		$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$
3864.1.v.d	$3864$	$1$	3864.v	3864.v	$2$	$1$	$1$	$1.928$	$\Q$	$D_{3}$	$\Q(\sqrt{-966}) $	None	✓	$2$	$0$	$-1$	$1$	$1$	$1$		$1$		$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
3864.1.v.e	$3864$	$1$	3864.v	3864.v	$2$	$1$	$1$	$1.928$	$\Q$	$D_{3}$	$\Q(\sqrt{-966}) $	None	✓	$2$	$0$	$1$	$-1$	$-1$	$1$		$1$		$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots$
3864.1.v.f	$3864$	$1$	3864.v	3864.v	$2$	$1$	$1$	$1.928$	$\Q$	$D_{3}$	$\Q(\sqrt{-966}) $	None	✓	$2$	$0$	$1$	$-1$	$1$	$-1$		$1$		$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
3864.1.v.g	$3864$	$1$	3864.v	3864.v	$2$	$1$	$1$	$1.928$	$\Q$	$D_{3}$	$\Q(\sqrt{-966}) $	None	✓	$2$	$0$	$1$	$1$	$-1$	$1$		$1$		$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots$
3864.1.v.h	$3864$	$1$	3864.v	3864.v	$2$	$1$	$1$	$1.928$	$\Q$	$D_{3}$	$\Q(\sqrt{-966}) $	None	✓	$2$	$0$	$1$	$1$	$1$	$-1$		$1$		$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots$
3864.1.v.i	$3864$	$1$	3864.v	3864.v	$2$	$4$	$4$	$1.928$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+(-\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{5}+\cdots$
3864.1.v.j	$3864$	$1$	3864.v	3864.v	$2$	$4$	$4$	$1.928$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{2}q^{2}-\zeta_{8}^{3}q^{3}-q^{4}+(-\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{5}+\cdots$
3864.1.bx.a	$3864$	$1$	3864.bx	3864.ax	$6$	$2$	$1$	$1.928$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-138}) $	None		$4$	$0$	$-1$	$-1$	$0$	$-1$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+q^{6}+\cdots$
3864.1.bx.b	$3864$	$1$	3864.bx	3864.ax	$6$	$2$	$1$	$1.928$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-138}) $	None		$4$	$0$	$-1$	$-1$	$0$	$1$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+q^{6}+\cdots$
3864.1.bx.c	$3864$	$1$	3864.bx	3864.ax	$6$	$2$	$1$	$1.928$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-138}) $	None		$4$	$0$	$1$	$-1$	$0$	$-1$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-q^{6}+\cdots$
3864.1.bx.d	$3864$	$1$	3864.bx	3864.ax	$6$	$2$	$1$	$1.928$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-138}) $	None		$4$	$0$	$1$	$-1$	$0$	$1$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-q^{6}+\cdots$
3864.1.bx.e	$3864$	$1$	3864.bx	3864.ax	$6$	$4$	$2$	$1.928$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-138}) $	None		$8$	$0$	$-2$	$2$	$0$	$0$		$1$		$q+\zeta_{12}^{4}q^{2}+\zeta_{12}^{2}q^{3}-\zeta_{12}^{2}q^{4}+\cdots$
3864.1.bx.f	$3864$	$1$	3864.bx	3864.ax	$6$	$4$	$2$	$1.928$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-138}) $	None		$8$	$0$	$2$	$2$	$0$	$0$		$1$		$q-\zeta_{12}^{4}q^{2}+\zeta_{12}^{2}q^{3}-\zeta_{12}^{2}q^{4}+\cdots$
3864.1.cx.a	$3864$	$1$	3864.cx	3864.bx	$22$	$40$	$4$	$1.928$	$\Q(\zeta_{88})$	$D_{44}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{88}^{42}q^{2}-\zeta_{88}^{23}q^{3}-\zeta_{88}^{40}q^{4}+\cdots$
3864.1.cx.b	$3864$	$1$	3864.cx	3864.bx	$22$	$40$	$4$	$1.928$	$\Q(\zeta_{88})$	$D_{44}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{88}^{6}q^{2}-\zeta_{88}^{11}q^{3}+\zeta_{88}^{12}q^{4}+\cdots$
3864.1.dl.a	$3864$	$1$	3864.dl	3864.cl	$22$	$10$	$1$	$1.928$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-42}) $	None		$4$	$0$	$-1$	$-1$	$0$	$-1$		$1$		$q-\zeta_{22}^{5}q^{2}-\zeta_{22}^{7}q^{3}+\zeta_{22}^{10}q^{4}+\cdots$
3864.1.dl.b	$3864$	$1$	3864.dl	3864.cl	$22$	$10$	$1$	$1.928$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-42}) $	None		$4$	$0$	$-1$	$1$	$0$	$1$		$1$		$q-\zeta_{22}^{5}q^{2}+\zeta_{22}^{7}q^{3}+\zeta_{22}^{10}q^{4}+\cdots$
3864.1.dl.c	$3864$	$1$	3864.dl	3864.cl	$22$	$10$	$1$	$1.928$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-42}) $	None		$4$	$0$	$1$	$-1$	$0$	$1$		$1$		$q+\zeta_{22}^{5}q^{2}-\zeta_{22}^{7}q^{3}+\zeta_{22}^{10}q^{4}+\cdots$
3864.1.dl.d	$3864$	$1$	3864.dl	3864.cl	$22$	$10$	$1$	$1.928$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-42}) $	None		$4$	$0$	$1$	$1$	$0$	$-1$		$1$		$q+\zeta_{22}^{5}q^{2}+\zeta_{22}^{7}q^{3}+\zeta_{22}^{10}q^{4}+\cdots$
3864.2.a.a	$3864$	$2$	3864.a	1.a	$1$	$1$	$1$	$30.854$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$-3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}-q^{7}+q^{9}-q^{13}+3q^{15}+\cdots$
3864.2.a.b	$3864$	$2$	3864.a	1.a	$1$	$1$	$1$	$30.854$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots$
3864.2.a.c	$3864$	$2$	3864.a	1.a	$1$	$1$	$1$	$30.854$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+q^{11}-6q^{13}+7q^{19}+\cdots$
3864.2.a.d	$3864$	$2$	3864.a	1.a	$1$	$1$	$1$	$30.854$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{7}+q^{9}+6q^{13}+2q^{15}+\cdots$
3864.2.a.e	$3864$	$2$	3864.a	1.a	$1$	$1$	$1$	$30.854$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{7}+q^{9}+4q^{11}+4q^{13}+\cdots$
3864.2.a.f	$3864$	$2$	3864.a	1.a	$1$	$1$	$1$	$30.854$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{5}+q^{7}+q^{9}+3q^{11}-2q^{13}+\cdots$
3864.2.a.g	$3864$	$2$	3864.a	1.a	$1$	$2$	$2$	$30.854$	$\Q(\sqrt{41}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-\beta q^{11}+2q^{13}+\cdots$
3864.2.a.h	$3864$	$2$	3864.a	1.a	$1$	$2$	$2$	$30.854$	$\Q(\sqrt{29}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}-q^{7}+q^{9}+5q^{11}+(1+\cdots)q^{13}+\cdots$
3864.2.a.i	$3864$	$2$	3864.a	1.a	$1$	$2$	$2$	$30.854$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}+q^{7}+q^{9}+(1-\beta )q^{11}+\cdots$
3864.2.a.j	$3864$	$2$	3864.a	1.a	$1$	$2$	$2$	$30.854$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$2$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-\beta q^{5}+q^{7}+q^{9}+(-3+2\beta )q^{11}+\cdots$
3864.2.a.k	$3864$	$2$	3864.a	1.a	$1$	$3$	$3$	$30.854$	3.3.621.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta _{1}+\beta _{2})q^{5}+q^{7}+q^{9}+\cdots$
3864.2.a.l	$3864$	$2$	3864.a	1.a	$1$	$3$	$3$	$30.854$	3.3.229.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{2}q^{5}-q^{7}+q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots$
3864.2.a.m	$3864$	$2$	3864.a	1.a	$1$	$3$	$3$	$30.854$	3.3.837.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{1}q^{5}+q^{7}+q^{9}+(2-\beta _{1}+\cdots)q^{11}+\cdots$
3864.2.a.n	$3864$	$2$	3864.a	1.a	$1$	$3$	$3$	$30.854$	3.3.1229.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{1}q^{5}+q^{7}+q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots$
3864.2.a.o	$3864$	$2$	3864.a	1.a	$1$	$3$	$3$	$30.854$	3.3.733.1	$_{}$	None	None	✓	$1$	$1$	$0$	$3$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta _{2})q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
3864.2.a.p	$3864$	$2$	3864.a	1.a	$1$	$3$	$3$	$30.854$	3.3.229.1	$_{}$	None	None	✓	$1$	$1$	$0$	$3$	$-3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1+\beta _{1})q^{5}+q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
3864.2.a.q	$3864$	$2$	3864.a	1.a	$1$	$3$	$3$	$30.854$	3.3.229.1	$_{}$	None	None	✓	$1$	$1$	$0$	$3$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-\beta _{2}q^{5}-q^{7}+q^{9}+(-1-\beta _{1}+\cdots)q^{11}+\cdots$
3864.2.a.r	$3864$	$2$	3864.a	1.a	$1$	$4$	$4$	$30.854$	4.4.2225.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-4$	$-3$	$4$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta _{3})q^{5}+q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots$
3864.2.a.s	$3864$	$2$	3864.a	1.a	$1$	$4$	$4$	$30.854$	4.4.75645.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-4$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{1}q^{5}-q^{7}+q^{9}+(-1-\beta _{1}+\cdots)q^{11}+\cdots$
3864.2.a.t	$3864$	$2$	3864.a	1.a	$1$	$4$	$4$	$30.854$	4.4.39605.1	$_{}$	None	None	✓	$1$	$0$	$0$	$4$	$-2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1+\beta _{1})q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
3864.2.a.u	$3864$	$2$	3864.a	1.a	$1$	$4$	$4$	$30.854$	4.4.256549.1	$_{}$	None	None	✓	$1$	$0$	$0$	$4$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{1}q^{5}+q^{7}+q^{9}+(-1-\beta _{2}+\cdots)q^{11}+\cdots$
3864.2.a.v	$3864$	$2$	3864.a	1.a	$1$	$5$	$5$	$30.854$	5.5.17679757.1	$_{}$	None	None	✓	$1$	$0$	$0$	$5$	$-6$	$5$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta _{1})q^{5}+q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$
3864.2.a.w	$3864$	$2$	3864.a	1.a	$1$	$6$	$6$	$30.854$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$-6$	$2$	$-6$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{3}q^{5}-q^{7}+q^{9}+\beta _{4}q^{11}+\cdots$
3864.2.a.x	$3864$	$2$	3864.a	1.a	$1$	$6$	$6$	$30.854$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$6$	$0$	$-6$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{5}q^{5}-q^{7}+q^{9}+(1+\beta _{4}+\cdots)q^{11}+\cdots$
3864.2.u.a	$3864$	$2$	3864.u	161.c	$2$	$4$	$4$	$30.854$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$1$	$0$	$0$	$-6$	$6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+(-2-\beta _{2})q^{5}+(1+\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
3864.2.u.b	$3864$	$2$	3864.u	161.c	$2$	$4$	$4$	$30.854$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$6$	$-6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+(2+\beta _{2})q^{5}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
3864.2.u.c	$3864$	$2$	3864.u	161.c	$2$	$8$	$8$	$30.854$	8.0.2992527616.3	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$2$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{3}+\beta _{3}q^{5}+(\beta _{1}+\beta _{4})q^{7}-q^{9}+\cdots$
3864.2.u.d	$3864$	$2$	3864.u	161.c	$2$	$8$	$8$	$30.854$	8.0.342102016.5	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}-\beta _{2}q^{5}+(-\beta _{4}+\beta _{6})q^{7}+\cdots$

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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.