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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 3645 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
124.1.i.a	$124$	$1$	124.i	124.i	$6$	$4$	$2$	$0.062$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-\zeta_{12}^{3}q^{2}-\zeta_{12}q^{3}-q^{4}-\zeta_{12}^{2}q^{5}+\cdots$
133.1.m.a	$133$	$1$	133.m	133.m	$6$	$4$	$2$	$0.066$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{5}q^{5}+\cdots$
171.1.o.a	$171$	$1$	171.o	171.o	$6$	$4$	$2$	$0.085$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$-2$	$-2$	$1$		$q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{3}q^{3}+\zeta_{12}^{4}q^{5}+\cdots$
201.1.g.a	$201$	$1$	201.g	201.g	$6$	$4$	$2$	$0.100$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{3}q^{3}-\zeta_{12}^{2}q^{6}+\cdots$
209.1.h.a	$209$	$1$	209.h	209.h	$6$	$4$	$2$	$0.104$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$-2$	$-2$	$0$	$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{2}q^{3}-\zeta_{12}^{2}q^{5}+\cdots$
219.1.j.b	$219$	$1$	219.j	219.j	$6$	$4$	$2$	$0.109$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{5}q^{5}+\zeta_{12}^{4}q^{6}+\cdots$
224.1.r.a	$224$	$1$	224.r	28.g	$6$	$4$	$2$	$0.112$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+\zeta_{12}^{5}q^{3}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{3}q^{7}+\cdots$
255.1.y.a	$255$	$1$	255.y	255.y	$8$	$8$	$2$	$0.127$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{16}-\zeta_{16}^{3})q^{2}-\zeta_{16}^{7}q^{3}+(\zeta_{16}^{2}+\cdots)q^{4}+\cdots$
273.1.s.b	$273$	$1$	273.s	273.s	$6$	$4$	$2$	$0.136$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-\zeta_{12}^{3}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{5}q^{5}+\cdots$
273.1.bm.b	$273$	$1$	273.bm	273.am	$6$	$4$	$2$	$0.136$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$4$	$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{5}q^{5}+\zeta_{12}^{4}q^{6}+\cdots$
288.1.o.a	$288$	$1$	288.o	36.f	$6$	$4$	$2$	$0.144$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q-\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{5}+\zeta_{12}q^{7}-q^{9}+\cdots$
301.1.r.a	$301$	$1$	301.r	301.r	$6$	$4$	$2$	$0.150$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{5}q^{3}-\zeta_{12}q^{5}-q^{6}+\cdots$
309.1.h.a	$309$	$1$	309.h	309.h	$6$	$4$	$2$	$0.154$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$-4$	$0$	$2$	$1$		$q-\zeta_{12}q^{2}-q^{3}+\zeta_{12}^{5}q^{5}+\zeta_{12}q^{6}+\cdots$
333.1.p.a	$333$	$1$	333.p	111.i	$6$	$4$	$2$	$0.166$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots$
344.1.l.b	$344$	$1$	344.l	344.l	$6$	$4$	$2$	$0.172$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q-\zeta_{12}^{3}q^{2}-\zeta_{12}^{4}q^{3}-q^{4}-\zeta_{12}q^{5}+\cdots$
385.1.q.c	$385$	$1$	385.q	385.q	$6$	$4$	$2$	$0.192$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$2$	$0$	$1$		$q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{2}+(-1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots$
392.1.k.b	$392$	$1$	392.k	56.k	$6$	$4$	$2$	$0.196$	$\Q(\sqrt{2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$2$	$0$	$0$	$0$	$1$		$q-\beta _{2}q^{2}-\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+\beta _{3}q^{6}+\cdots$
399.1.n.a	$399$	$1$	399.n	399.n	$6$	$4$	$2$	$0.199$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$	$1$		$q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{3}q^{5}+\cdots$
399.1.bi.a	$399$	$1$	399.bi	399.ai	$6$	$4$	$2$	$0.199$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$	$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{5}q^{5}+\cdots$
25.2.e.a	$25$	$2$	25.e	25.e	$10$	$8$	$2$	$0.200$	8.0.58140625.2	$_{}$	None	None		$2$	$0$	$-5$	$-5$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-1+\beta _{1})q^{2}+(-1+\beta _{2}-\beta _{3}+\beta _{7})q^{3}+\cdots$
403.1.p.a	$403$	$1$	403.p	403.p	$6$	$4$	$2$	$0.201$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$-2$	$0$	$0$	$2$	$1$		$q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{5}q^{3}+\zeta_{12}q^{6}-\zeta_{12}^{4}q^{7}+\cdots$
416.1.bb.a	$416$	$1$	416.bb	52.j	$6$	$4$	$2$	$0.208$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{3}-\zeta_{12}^{5}q^{7}-\zeta_{12}q^{11}+q^{13}+\cdots$
420.1.be.a	$420$	$1$	420.be	420.ae	$6$	$4$	$2$	$0.210$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+\zeta_{12}q^{2}-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{4}q^{5}+\cdots$
420.1.be.b	$420$	$1$	420.be	420.ae	$6$	$4$	$2$	$0.210$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$2$	$0$	$1$		$q+\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{4}q^{5}+\cdots$
429.1.v.c	$429$	$1$	429.v	429.v	$10$	$8$	$2$	$0.214$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$2$	$0$	$0$	$1$		$q+(-\zeta_{20}+\zeta_{20}^{5})q^{2}-\zeta_{20}^{4}q^{3}+(-1+\cdots)q^{4}+\cdots$
27.2.e.a	$27$	$2$	27.e	27.e	$9$	$12$	$2$	$0.216$	12.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$-6$	$-6$	$-3$	$-6$	$3$	$\mathrm{SU}(2)[C_{9}]$	$q+(-1-\beta _{3}+\beta _{8})q^{2}+(-1-\beta _{2}+\beta _{6}+\cdots)q^{3}+\cdots$
441.1.q.a	$441$	$1$	441.q	21.h	$6$	$4$	$2$	$0.220$	$\Q(\sqrt{-2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{3})q^{11}+\cdots$
28.2.f.a	$28$	$2$	28.f	28.f	$6$	$4$	$2$	$0.224$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$-2$	$0$	$-6$	$0$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}+\cdots)q^{3}+\cdots$
448.1.r.a	$448$	$1$	448.r	28.g	$6$	$4$	$2$	$0.224$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}-\zeta_{12}q^{11}+\cdots$
453.1.h.a	$453$	$1$	453.h	453.h	$6$	$4$	$2$	$0.226$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$-4$	$0$	$-2$	$1$		$q+\zeta_{12}^{5}q^{2}-q^{3}+\zeta_{12}^{5}q^{5}-\zeta_{12}^{5}q^{6}+\cdots$
455.1.be.a	$455$	$1$	455.be	455.ae	$6$	$4$	$2$	$0.227$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-35}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{12}+\zeta_{12}^{3})q^{3}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{3}q^{5}+\cdots$
468.1.q.a	$468$	$1$	468.q	52.i	$6$	$4$	$2$	$0.234$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}-\zeta_{12}^{3}q^{8}+\cdots$
468.1.r.a	$468$	$1$	468.r	39.i	$6$	$4$	$2$	$0.234$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-\beta _{3}q^{5}+(-1+\beta _{2})q^{7}+(\beta _{1}-\beta _{3})q^{11}+\cdots$
468.1.v.a	$468$	$1$	468.v	468.v	$6$	$4$	$2$	$0.234$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q-\zeta_{12}q^{2}+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{4}q^{5}+\cdots$
468.1.y.a	$468$	$1$	468.y	468.y	$6$	$4$	$2$	$0.234$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{3}q^{3}-q^{4}-\zeta_{12}^{4}q^{5}+\cdots$
476.1.o.c	$476$	$1$	476.o	476.o	$6$	$4$	$2$	$0.238$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-17}) $	None		$8$	$0$	$2$	$0$	$0$	$0$	$1$		$q+\zeta_{12}^{2}q^{2}+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{3}+\cdots$
480.1.bu.a	$480$	$1$	480.bu	480.au	$8$	$8$	$2$	$0.240$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}^{3}q^{2}-\zeta_{16}^{7}q^{3}+\zeta_{16}^{6}q^{4}+\cdots$
497.1.g.a	$497$	$1$	497.g	497.g	$6$	$4$	$2$	$0.248$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$-2$	$2$	$-2$	$0$	$1$		$q-\zeta_{12}^{2}q^{2}-\zeta_{12}^{4}q^{3}-\zeta_{12}^{2}q^{5}+\cdots$
500.1.h.a	$500$	$1$	500.h	100.h	$10$	$8$	$2$	$0.250$	$\Q(\zeta_{20})$	$D_{5}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{20}q^{2}+\zeta_{20}^{2}q^{4}-\zeta_{20}^{3}q^{8}-\zeta_{20}^{4}q^{9}+\cdots$
504.1.ba.a	$504$	$1$	504.ba	504.aa	$6$	$4$	$2$	$0.252$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{3}-\zeta_{12}^{4}q^{4}+\cdots$
504.1.bn.c	$504$	$1$	504.bn	504.an	$6$	$4$	$2$	$0.252$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$2$	$0$	$0$	$2$	$1$		$q+\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{4}q^{4}+\cdots$
504.1.bw.a	$504$	$1$	504.bw	56.j	$6$	$4$	$2$	$0.252$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+(\zeta_{12}+\zeta_{12}^{3}+\cdots)q^{5}+\cdots$
504.1.ce.a	$504$	$1$	504.ce	504.be	$6$	$4$	$2$	$0.252$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$-4$	$0$	$0$	$1$		$q-\zeta_{12}^{3}q^{2}-q^{3}-q^{4}+\zeta_{12}q^{5}+\zeta_{12}^{3}q^{6}+\cdots$
504.1.cu.a	$504$	$1$	504.cu	21.h	$6$	$4$	$2$	$0.252$	$\Q(\sqrt{-2}, \sqrt{-3})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+(\beta _{1}-\beta _{3})q^{5}+\beta _{2}q^{7}-\beta _{1}q^{11}-q^{13}+\cdots$
32.2.g.b	$32$	$2$	32.g	32.g	$8$	$8$	$2$	$0.256$	8.0.18939904.2	$_{}$	None	None		$2$	$0$	$-4$	$-4$	$0$	$-8$	$2$	$\mathrm{SU}(2)[C_{8}]$	$q-\beta _{2}q^{2}+(\beta _{1}+\beta _{3}+\beta _{5}+\beta _{7})q^{3}+\cdots$
513.1.o.a	$513$	$1$	513.o	171.o	$6$	$4$	$2$	$0.256$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$2$	$-2$	$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{5}+\zeta_{12}^{4}q^{7}+\zeta_{12}^{3}q^{8}+\cdots$
520.1.cd.a	$520$	$1$	520.cd	520.bd	$6$	$4$	$2$	$0.260$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-10}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{3}q^{5}+\cdots$
525.1.p.a	$525$	$1$	525.p	105.o	$6$	$4$	$2$	$0.262$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{3}-\zeta_{12}^{4}q^{4}+\zeta_{12}q^{7}+\zeta_{12}^{2}q^{9}+\cdots$
33.2.f.a	$33$	$2$	33.f	33.f	$10$	$8$	$2$	$0.264$	$\Q(\zeta_{20})$	$_{}$	None	None		$4$	$0$	$0$	$-6$	$0$	$-10$	$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-\zeta_{20}^{5}-\zeta_{20}^{7})q^{2}+(-1+\zeta_{20}+\cdots)q^{3}+\cdots$
532.1.n.a	$532$	$1$	532.n	532.n	$6$	$4$	$2$	$0.266$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{4}q^{4}+\cdots$

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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.