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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 2534 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
116.1.j.a	$116$	$1$	116.j	116.j	$14$	$6$	$1$	$0.058$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{14}q^{2}+\zeta_{14}^{2}q^{4}+(\zeta_{14}^{4}-\zeta_{14}^{5}+\cdots)q^{5}+\cdots$
129.1.l.a	$129$	$1$	129.l	129.l	$14$	$6$	$1$	$0.064$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{14}^{5}q^{3}+\zeta_{14}^{4}q^{4}+(-\zeta_{14}+\zeta_{14}^{6}+\cdots)q^{7}+\cdots$
147.1.l.a	$147$	$1$	147.l	147.l	$14$	$6$	$1$	$0.073$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-1$	$1$		$q+\zeta_{14}^{2}q^{3}+\zeta_{14}^{6}q^{4}-\zeta_{14}^{3}q^{7}+\cdots$
148.1.p.a	$148$	$1$	148.p	148.p	$18$	$6$	$1$	$0.074$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-3$	$0$	$1$		$q-\zeta_{18}q^{2}+\zeta_{18}^{2}q^{4}+(\zeta_{18}^{4}+\zeta_{18}^{6}+\cdots)q^{5}+\cdots$
152.1.u.a	$152$	$1$	152.u	152.u	$18$	$6$	$1$	$0.076$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-3$	$0$	$0$	$1$		$q-\zeta_{18}^{5}q^{2}+(\zeta_{18}^{6}-\zeta_{18}^{7})q^{3}-\zeta_{18}q^{4}+\cdots$
203.1.n.a	$203$	$1$	203.n	203.n	$14$	$6$	$1$	$0.101$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$	$1$		$q+(-\zeta_{14}^{3}+\zeta_{14}^{6})q^{2}+(\zeta_{14}^{2}-\zeta_{14}^{5}+\cdots)q^{4}+\cdots$
203.1.o.a	$203$	$1$	203.o	203.o	$14$	$6$	$1$	$0.101$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$1$	$1$		$q+(\zeta_{14}^{5}+\zeta_{14}^{6})q^{2}+(-\zeta_{14}^{3}-\zeta_{14}^{4}+\cdots)q^{4}+\cdots$
216.1.r.a	$216$	$1$	216.r	216.r	$18$	$6$	$1$	$0.108$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{2}q^{2}+\zeta_{18}^{8}q^{3}+\zeta_{18}^{4}q^{4}+\cdots$
219.1.o.a	$219$	$1$	219.o	219.o	$12$	$4$	$1$	$0.109$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+\zeta_{12}^{3}q^{3}-\zeta_{12}^{2}q^{4}+(\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{7}+\cdots$
228.1.s.a	$228$	$1$	228.s	57.l	$18$	$6$	$1$	$0.114$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{8}q^{3}+(\zeta_{18}^{2}+\zeta_{18}^{4})q^{7}-\zeta_{18}^{7}q^{9}+\cdots$
259.1.bi.a	$259$	$1$	259.bi	259.ai	$18$	$6$	$1$	$0.129$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}^{3}+\zeta_{18}^{4})q^{2}+(\zeta_{18}^{6}-\zeta_{18}^{7}+\cdots)q^{4}+\cdots$
259.1.bo.a	$259$	$1$	259.bo	259.ao	$18$	$6$	$1$	$0.129$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{3}-\zeta_{18}^{7})q^{2}+(\zeta_{18}-\zeta_{18}^{5}+\cdots)q^{4}+\cdots$
260.1.be.a	$260$	$1$	260.be	260.ae	$12$	$4$	$1$	$0.130$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}-\zeta_{12}^{5}q^{5}+\cdots$
260.1.bl.a	$260$	$1$	260.bl	260.al	$12$	$4$	$1$	$0.130$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{8}+\cdots$
273.1.bs.a	$273$	$1$	273.bs	273.as	$12$	$4$	$1$	$0.136$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{12}q^{3}-\zeta_{12}^{3}q^{4}-\zeta_{12}q^{7}+\zeta_{12}^{2}q^{9}+\cdots$
273.1.ch.a	$273$	$1$	273.ch	273.bh	$12$	$4$	$1$	$0.136$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-\zeta_{12}^{3}q^{3}-\zeta_{12}^{5}q^{4}+\zeta_{12}^{4}q^{7}+\cdots$
285.1.bd.a	$285$	$1$	285.bd	285.ad	$18$	$6$	$1$	$0.142$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}+\zeta_{18}^{6})q^{2}+\zeta_{18}^{2}q^{3}+(-\zeta_{18}+\cdots)q^{4}+\cdots$
285.1.bd.b	$285$	$1$	285.bd	285.ad	$18$	$6$	$1$	$0.142$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}^{4}-\zeta_{18}^{6})q^{2}-\zeta_{18}^{2}q^{3}+\cdots$
291.1.o.a	$291$	$1$	291.o	291.o	$16$	$8$	$1$	$0.145$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}q^{3}+\zeta_{16}^{6}q^{4}+(-\zeta_{16}+\zeta_{16}^{4}+\cdots)q^{7}+\cdots$
292.1.q.a	$292$	$1$	292.q	292.q	$18$	$6$	$1$	$0.146$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{2}q^{2}+\zeta_{18}^{4}q^{4}+(-\zeta_{18}-\zeta_{18}^{4}+\cdots)q^{5}+\cdots$
292.1.r.a	$292$	$1$	292.r	292.r	$18$	$6$	$1$	$0.146$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{7}q^{2}-\zeta_{18}^{5}q^{4}-\zeta_{18}^{2}q^{5}+\cdots$
297.1.q.a	$297$	$1$	297.q	297.q	$18$	$6$	$1$	$0.148$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$-3$	$0$	$1$		$q+\zeta_{18}^{8}q^{3}+\zeta_{18}^{2}q^{4}+(-\zeta_{18}^{3}-\zeta_{18}^{7}+\cdots)q^{5}+\cdots$
301.1.v.a	$301$	$1$	301.v	301.v	$14$	$6$	$1$	$0.150$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$6$	$1$		$q+(-\zeta_{14}-\zeta_{14}^{3})q^{2}+(\zeta_{14}^{2}+\zeta_{14}^{4}+\cdots)q^{4}+\cdots$
327.1.n.a	$327$	$1$	327.n	327.n	$18$	$6$	$1$	$0.163$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-3$	$1$		$q+\zeta_{18}^{7}q^{3}-\zeta_{18}^{6}q^{4}+(\zeta_{18}^{2}+\zeta_{18}^{6}+\cdots)q^{7}+\cdots$
327.1.o.a	$327$	$1$	327.o	327.o	$18$	$6$	$1$	$0.163$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-3$	$1$		$q+\zeta_{18}^{4}q^{3}+\zeta_{18}^{6}q^{4}+(-\zeta_{18}^{5}+\zeta_{18}^{6}+\cdots)q^{7}+\cdots$
328.1.z.a	$328$	$1$	328.z	328.z	$20$	$8$	$1$	$0.164$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+\zeta_{20}^{7}q^{2}+(-\zeta_{20}^{2}+\zeta_{20}^{3})q^{3}+\cdots$
333.1.bb.a	$333$	$1$	333.bb	37.g	$12$	$4$	$1$	$0.166$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{12}^{5}q^{4}+(\zeta_{12}+\zeta_{12}^{3})q^{7}+(-\zeta_{12}^{3}+\cdots)q^{13}+\cdots$
340.1.bc.a	$340$	$1$	340.bc	340.ac	$16$	$8$	$1$	$0.170$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}-\zeta_{16}^{6}q^{5}+\cdots$
340.1.bj.a	$340$	$1$	340.bj	340.aj	$16$	$8$	$1$	$0.170$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}+\zeta_{16}^{3}q^{5}+\cdots$
344.1.s.a	$344$	$1$	344.s	344.s	$14$	$6$	$1$	$0.172$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q+\zeta_{14}^{2}q^{2}+(-\zeta_{14}+\zeta_{14}^{2})q^{3}+\zeta_{14}^{4}q^{4}+\cdots$
351.1.bg.a	$351$	$1$	351.bg	13.f	$12$	$4$	$1$	$0.175$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+\zeta_{12}^{5}q^{4}+(\zeta_{12}^{2}-\zeta_{12}^{5})q^{7}+\zeta_{12}^{3}q^{13}+\cdots$
23.2.c.a	$23$	$2$	23.c	23.c	$11$	$10$	$1$	$0.184$	$\Q(\zeta_{22})$	$_{}$	None	None		$2$	$0$	$-7$	$-7$	$-3$	$-5$	$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(-\zeta_{22}+\zeta_{22}^{4}-\zeta_{22}^{5}+\zeta_{22}^{6}+\cdots)q^{2}+\cdots$
371.1.k.a	$371$	$1$	371.k	371.k	$12$	$4$	$1$	$0.185$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$-2$	$-2$	$2$	$0$	$1$		$q+(-\zeta_{12}^{2}+\zeta_{12}^{5})q^{2}+(\zeta_{12}+\zeta_{12}^{4}+\cdots)q^{3}+\cdots$
371.1.k.b	$371$	$1$	371.k	371.k	$12$	$4$	$1$	$0.185$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q-\zeta_{12}q^{4}+(\zeta_{12}^{2}+\zeta_{12}^{5})q^{5}+\zeta_{12}q^{7}+\cdots$
380.1.x.a	$380$	$1$	380.x	95.m	$12$	$4$	$1$	$0.190$	$\Q(\zeta_{12})$	$S_{4}$	None	None		$4$	$0$	$0$	$-2$	$2$	$0$	$1$		$q+(-\zeta_{12}^{2}+\zeta_{12}^{5})q^{3}+\zeta_{12}^{2}q^{5}+\cdots$
381.1.m.a	$381$	$1$	381.m	381.m	$14$	$6$	$1$	$0.190$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$5$	$1$		$q+\zeta_{14}^{6}q^{3}-\zeta_{14}^{3}q^{4}+(1-\zeta_{14})q^{7}+\cdots$
387.1.w.a	$387$	$1$	387.w	43.f	$14$	$6$	$1$	$0.193$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{14}q^{4}+(-\zeta_{14}^{2}-\zeta_{14}^{5})q^{7}+(-\zeta_{14}^{4}+\cdots)q^{13}+\cdots$
388.1.m.a	$388$	$1$	388.m	388.m	$12$	$4$	$1$	$0.194$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-\zeta_{12}^{2}-\zeta_{12}^{3}+\cdots)q^{5}+\cdots$
399.1.bs.a	$399$	$1$	399.bs	399.as	$18$	$6$	$1$	$0.199$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{5}q^{3}-\zeta_{18}^{4}q^{4}+\zeta_{18}^{2}q^{7}+\cdots$
399.1.by.a	$399$	$1$	399.by	399.ay	$18$	$6$	$1$	$0.199$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{5}q^{3}+\zeta_{18}q^{4}-\zeta_{18}^{7}q^{7}-\zeta_{18}q^{9}+\cdots$
399.1.ca.a	$399$	$1$	399.ca	399.ba	$18$	$6$	$1$	$0.199$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{2}q^{3}-\zeta_{18}^{7}q^{4}+\zeta_{18}^{8}q^{7}+\cdots$
399.1.ch.a	$399$	$1$	399.ch	399.bh	$18$	$6$	$1$	$0.199$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{7}q^{3}-\zeta_{18}^{5}q^{4}+\zeta_{18}^{8}q^{7}+\cdots$
407.1.t.a	$407$	$1$	407.t	407.t	$18$	$6$	$1$	$0.203$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-3$	$0$	$0$	$1$		$q+(\zeta_{18}^{2}+\zeta_{18}^{6})q^{3}-\zeta_{18}q^{4}+\zeta_{18}^{7}q^{5}+\cdots$
407.1.u.a	$407$	$1$	407.u	407.u	$18$	$6$	$1$	$0.203$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$3$	$0$	$0$	$1$		$q+(-\zeta_{18}^{6}-\zeta_{18}^{8})q^{3}-\zeta_{18}^{4}q^{4}+\cdots$
408.1.bg.a	$408$	$1$	408.bg	408.ag	$16$	$8$	$1$	$0.204$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{16}q^{2}+\zeta_{16}^{6}q^{3}+\zeta_{16}^{2}q^{4}-\zeta_{16}^{7}q^{6}+\cdots$
408.1.bg.b	$408$	$1$	408.bg	408.ag	$16$	$8$	$1$	$0.204$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}q^{2}+\zeta_{16}^{5}q^{3}+\zeta_{16}^{2}q^{4}+\zeta_{16}^{6}q^{6}+\cdots$
416.1.bl.a	$416$	$1$	416.bl	13.f	$12$	$4$	$1$	$0.208$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+(\zeta_{12}^{4}+\zeta_{12}^{5})q^{5}+\zeta_{12}^{2}q^{9}+\zeta_{12}q^{13}+\cdots$
436.1.n.a	$436$	$1$	436.n	436.n	$18$	$6$	$1$	$0.218$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{3}q^{2}+\zeta_{18}^{6}q^{4}+\zeta_{18}q^{5}+q^{8}+\cdots$
441.1.v.a	$441$	$1$	441.v	49.f	$14$	$6$	$1$	$0.220$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$1$	$1$		$q-\zeta_{14}^{4}q^{4}-\zeta_{14}^{2}q^{7}+(\zeta_{14}-\zeta_{14}^{3}+\cdots)q^{13}+\cdots$
444.1.bc.a	$444$	$1$	444.bc	111.n	$18$	$6$	$1$	$0.222$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$3$	$1$		$q-\zeta_{18}^{7}q^{3}+(\zeta_{18}^{5}-\zeta_{18}^{6})q^{7}-\zeta_{18}^{5}q^{9}+\cdots$

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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.