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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 106 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
3240.1.p.a	$3240$	$1$	3240.p	40.e	$2$	$1$	$1$	$1.617$	$\Q$	$D_{3}$	$\Q(\sqrt{-10}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-1$		$1$		$q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots$
3240.1.p.b	$3240$	$1$	3240.p	40.e	$2$	$1$	$1$	$1.617$	$\Q$	$D_{3}$	$\Q(\sqrt{-10}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$1$		$1$		$q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots$
3240.1.p.c	$3240$	$1$	3240.p	40.e	$2$	$1$	$1$	$1.617$	$\Q$	$D_{3}$	$\Q(\sqrt{-10}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$-1$		$1$		$q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots$
3240.1.p.d	$3240$	$1$	3240.p	40.e	$2$	$1$	$1$	$1.617$	$\Q$	$D_{3}$	$\Q(\sqrt{-10}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$1$		$1$		$q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots$
3240.1.p.e	$3240$	$1$	3240.p	40.e	$2$	$2$	$2$	$1.617$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-10}) $	None	✓	$4$	$0$	$-2$	$0$	$2$	$0$		$1$		$q-q^{2}+q^{4}+q^{5}-\beta q^{7}-q^{8}-q^{10}+\cdots$
3240.1.p.f	$3240$	$1$	3240.p	40.e	$2$	$2$	$2$	$1.617$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-10}) $	None	✓	$4$	$0$	$2$	$0$	$-2$	$0$		$1$		$q+q^{2}+q^{4}-q^{5}-\beta q^{7}+q^{8}-q^{10}+\cdots$
3240.1.v.a	$3240$	$1$	3240.v	5.c	$4$	$2$	$1$	$1.617$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-q^{5}+q^{11}+iq^{19}+(-1-i)q^{23}+\cdots$
3240.1.v.b	$3240$	$1$	3240.v	5.c	$4$	$2$	$1$	$1.617$	$\Q(\sqrt{-1}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$1$		$q+q^{5}-q^{11}+iq^{19}+(1+i)q^{23}+\cdots$
3240.1.z.a	$3240$	$1$	3240.z	360.z	$6$	$2$	$1$	$1.617$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-2$	$0$	$-1$	$0$		$1$		$q-q^{2}+q^{4}+\zeta_{6}^{2}q^{5}-q^{8}-\zeta_{6}^{2}q^{10}+\cdots$
3240.1.z.b	$3240$	$1$	3240.z	360.z	$6$	$2$	$1$	$1.617$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$-1$	$0$	$-1$	$-1$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots$
3240.1.z.c	$3240$	$1$	3240.z	360.z	$6$	$2$	$1$	$1.617$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$-1$	$0$	$-1$	$1$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots$
3240.1.z.d	$3240$	$1$	3240.z	360.z	$6$	$2$	$1$	$1.617$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-10}) $	$\Q(\sqrt{6}) $		$8$	$0$	$-1$	$0$	$1$	$0$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+q^{8}+\cdots$
3240.1.z.e	$3240$	$1$	3240.z	360.z	$6$	$2$	$1$	$1.617$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-1$	$0$	$1$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+q^{8}+\cdots$
3240.1.z.f	$3240$	$1$	3240.z	360.z	$6$	$2$	$1$	$1.617$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-10}) $	$\Q(\sqrt{6}) $		$8$	$0$	$1$	$0$	$-1$	$0$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}-q^{8}+\cdots$
3240.1.z.g	$3240$	$1$	3240.z	360.z	$6$	$2$	$1$	$1.617$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$1$	$0$	$-1$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}-q^{8}+\cdots$
3240.1.z.h	$3240$	$1$	3240.z	360.z	$6$	$2$	$1$	$1.617$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$1$	$0$	$1$	$-1$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots$
3240.1.z.i	$3240$	$1$	3240.z	360.z	$6$	$2$	$1$	$1.617$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$1$	$0$	$1$	$1$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots$
3240.1.z.j	$3240$	$1$	3240.z	360.z	$6$	$2$	$1$	$1.617$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$2$	$0$	$1$	$0$		$1$		$q+q^{2}+q^{4}-\zeta_{6}^{2}q^{5}+q^{8}-\zeta_{6}^{2}q^{10}+\cdots$
3240.1.z.k	$3240$	$1$	3240.z	360.z	$6$	$4$	$2$	$1.617$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-10}) $	None		$8$	$0$	$-2$	$0$	$2$	$0$		$3$		$q+\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{4}+\zeta_{12}^{2}q^{5}+\cdots$
3240.1.z.l	$3240$	$1$	3240.z	360.z	$6$	$4$	$2$	$1.617$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-10}) $	None		$8$	$0$	$2$	$0$	$-2$	$0$		$3$		$q-\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{4}-\zeta_{12}^{2}q^{5}+\cdots$
3240.1.bh.a	$3240$	$1$	3240.bh	360.ah	$6$	$2$	$1$	$1.617$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-30}) $	None		$4$	$0$	$-1$	$0$	$-1$	$0$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+q^{8}+\cdots$
3240.1.bh.b	$3240$	$1$	3240.bh	360.ah	$6$	$2$	$1$	$1.617$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-30}) $	None		$4$	$0$	$-1$	$0$	$1$	$0$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+q^{8}+\cdots$
3240.1.bh.c	$3240$	$1$	3240.bh	360.ah	$6$	$2$	$1$	$1.617$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-30}) $	None		$4$	$0$	$1$	$0$	$-1$	$0$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}-q^{8}+\cdots$
3240.1.bh.d	$3240$	$1$	3240.bh	360.ah	$6$	$2$	$1$	$1.617$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-30}) $	None		$4$	$0$	$1$	$0$	$1$	$0$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-q^{8}+\cdots$
3240.1.bh.e	$3240$	$1$	3240.bh	360.ah	$6$	$4$	$2$	$1.617$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{3}q^{2}-q^{4}-\zeta_{12}^{5}q^{5}+\zeta_{12}^{3}q^{8}+\cdots$
3240.1.bh.f	$3240$	$1$	3240.bh	360.ah	$6$	$4$	$2$	$1.617$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$-6$		$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}+(-1+\cdots)q^{7}+\cdots$
3240.1.bh.g	$3240$	$1$	3240.bh	360.ah	$6$	$4$	$2$	$1.617$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{5}q^{5}+\cdots$
3240.1.bh.h	$3240$	$1$	3240.bh	360.ah	$6$	$4$	$2$	$1.617$	$\Q(\zeta_{12})$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{10}) $		$16$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{5}-\zeta_{12}^{3}q^{8}+\cdots$
3240.1.bh.i	$3240$	$1$	3240.bh	360.ah	$6$	$4$	$2$	$1.617$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$6$		$1$		$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}q^{5}+(1+\cdots)q^{7}+\cdots$
3240.1.bn.a	$3240$	$1$	3240.bn	45.h	$6$	$8$	$4$	$1.617$	$\Q(\zeta_{24})$	$S_{4}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{24}^{7}q^{5}-\zeta_{24}^{2}q^{7}+(\zeta_{24}^{5}-\zeta_{24}^{11}+\cdots)q^{11}+\cdots$
3240.1.bq.a	$3240$	$1$	3240.bq	45.k	$12$	$4$	$1$	$1.617$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$		$1$		$q-\zeta_{12}^{2}q^{5}-\zeta_{12}^{4}q^{11}+\zeta_{12}^{3}q^{19}+\cdots$
3240.1.bq.b	$3240$	$1$	3240.bq	45.k	$12$	$4$	$1$	$1.617$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$2$	$0$		$1$		$q+\zeta_{12}^{2}q^{5}+\zeta_{12}^{4}q^{11}+\zeta_{12}^{3}q^{19}+\cdots$
3240.1.bv.a	$3240$	$1$	3240.bv	360.au	$12$	$8$	$2$	$1.617$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$-8$		$1$		$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}-\zeta_{24}q^{5}+(-1+\cdots)q^{7}+\cdots$
3240.1.bv.b	$3240$	$1$	3240.bv	360.au	$12$	$8$	$2$	$1.617$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$4$		$1$		$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}-\zeta_{24}^{9}q^{5}+\cdots$
3240.1.bv.c	$3240$	$1$	3240.bv	360.au	$12$	$8$	$2$	$1.617$	$\Q(\zeta_{24})$	$D_{4}$	$\Q(\sqrt{-6}) $	None		$16$	$0$	$0$	$0$	$0$	$4$		$1$		$q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}-\zeta_{24}^{5}q^{5}+\cdots$
3240.2.a.a	$3240$	$2$	3240.a	1.a	$1$	$1$	$1$	$25.872$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}+3q^{11}-2q^{17}+q^{19}+\cdots$
3240.2.a.b	$3240$	$2$	3240.a	1.a	$1$	$1$	$1$	$25.872$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-5q^{11}+3q^{17}+5q^{19}+6q^{23}+\cdots$
3240.2.a.c	$3240$	$2$	3240.a	1.a	$1$	$1$	$1$	$25.872$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+q^{11}-7q^{19}+6q^{23}+q^{25}+\cdots$
3240.2.a.d	$3240$	$2$	3240.a	1.a	$1$	$1$	$1$	$25.872$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-3q^{11}+2q^{17}+q^{19}+\cdots$
3240.2.a.e	$3240$	$2$	3240.a	1.a	$1$	$1$	$1$	$25.872$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{11}-7q^{19}-6q^{23}+q^{25}+\cdots$
3240.2.a.f	$3240$	$2$	3240.a	1.a	$1$	$1$	$1$	$25.872$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+5q^{11}-3q^{17}+5q^{19}-6q^{23}+\cdots$
3240.2.a.g	$3240$	$2$	3240.a	1.a	$1$	$2$	$2$	$25.872$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+(-1+\beta )q^{7}+(2+\beta )q^{11}+(-2+\cdots)q^{13}+\cdots$
3240.2.a.h	$3240$	$2$	3240.a	1.a	$1$	$2$	$2$	$25.872$	$\Q(\sqrt{57}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+\beta q^{7}+(-3+\beta )q^{11}+(2+\beta )q^{13}+\cdots$
3240.2.a.i	$3240$	$2$	3240.a	1.a	$1$	$2$	$2$	$25.872$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+\beta q^{7}+(1-\beta )q^{11}-\beta q^{13}+\cdots$
3240.2.a.j	$3240$	$2$	3240.a	1.a	$1$	$2$	$2$	$25.872$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+(1+\beta )q^{7}-2q^{17}+(-2-2\beta )q^{19}+\cdots$
3240.2.a.k	$3240$	$2$	3240.a	1.a	$1$	$2$	$2$	$25.872$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+(2+\beta )q^{7}+(2+2\beta )q^{11}+(-2+\cdots)q^{13}+\cdots$
3240.2.a.l	$3240$	$2$	3240.a	1.a	$1$	$2$	$2$	$25.872$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(-1+\beta )q^{7}+(-2-\beta )q^{11}+\cdots$
3240.2.a.m	$3240$	$2$	3240.a	1.a	$1$	$2$	$2$	$25.872$	$\Q(\sqrt{33}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+\beta q^{7}+(-1+\beta )q^{11}-\beta q^{13}+\cdots$
3240.2.a.n	$3240$	$2$	3240.a	1.a	$1$	$2$	$2$	$25.872$	$\Q(\sqrt{57}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+\beta q^{7}+(3-\beta )q^{11}+(2+\beta )q^{13}+\cdots$
3240.2.a.o	$3240$	$2$	3240.a	1.a	$1$	$2$	$2$	$25.872$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+(1+\beta )q^{7}+2q^{17}+(-2-2\beta )q^{19}+\cdots$

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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.