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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 402 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
259.1.bo.a	$259$	$1$	259.bo	259.ao	$18$	$6$	$1$	$0.129$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{3}-\zeta_{18}^{7})q^{2}+(\zeta_{18}-\zeta_{18}^{5}+\cdots)q^{4}+\cdots$
292.1.q.a	$292$	$1$	292.q	292.q	$18$	$6$	$1$	$0.146$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{2}q^{2}+\zeta_{18}^{4}q^{4}+(-\zeta_{18}-\zeta_{18}^{4}+\cdots)q^{5}+\cdots$
299.1.j.a	$299$	$1$	299.j	299.j	$6$	$6$	$3$	$0.149$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}-\zeta_{18}^{8})q^{2}+(\zeta_{18}^{5}+\zeta_{18}^{7}+\cdots)q^{3}+\cdots$
327.1.n.a	$327$	$1$	327.n	327.n	$18$	$6$	$1$	$0.163$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-3$	$1$		$q+\zeta_{18}^{7}q^{3}-\zeta_{18}^{6}q^{4}+(\zeta_{18}^{2}+\zeta_{18}^{6}+\cdots)q^{7}+\cdots$
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		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{5}q^{3}+\zeta_{18}q^{4}-\zeta_{18}^{7}q^{7}-\zeta_{18}q^{9}+\cdots$
407.1.u.a	$407$	$1$	407.u	407.u	$18$	$6$	$1$	$0.203$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$3$	$0$	$0$	$1$		$q+(-\zeta_{18}^{6}-\zeta_{18}^{8})q^{3}-\zeta_{18}^{4}q^{4}+\cdots$
444.1.bc.a	$444$	$1$	444.bc	111.n	$18$	$6$	$1$	$0.222$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$3$	$1$		$q-\zeta_{18}^{7}q^{3}+(\zeta_{18}^{5}-\zeta_{18}^{6})q^{7}-\zeta_{18}^{5}q^{9}+\cdots$
456.1.bt.a	$456$	$1$	456.bt	456.at	$18$	$6$	$1$	$0.228$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{5}q^{2}-\zeta_{18}^{7}q^{3}-\zeta_{18}q^{4}+\zeta_{18}^{3}q^{6}+\cdots$
456.1.bt.b	$456$	$1$	456.bt	456.at	$18$	$6$	$1$	$0.228$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$3$	$0$	$0$	$1$		$q-\zeta_{18}^{5}q^{2}-\zeta_{18}^{6}q^{3}-\zeta_{18}q^{4}-\zeta_{18}^{2}q^{6}+\cdots$
513.1.br.a	$513$	$1$	513.br	19.f	$18$	$6$	$1$	$0.256$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{4}q^{4}+(\zeta_{18}^{7}-\zeta_{18}^{8})q^{7}+(-1+\cdots)q^{13}+\cdots$
584.1.bd.a	$584$	$1$	584.bd	584.ad	$18$	$6$	$1$	$0.291$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{5}q^{2}+(-\zeta_{18}^{4}-\zeta_{18}^{8})q^{3}+\cdots$
592.1.bt.a	$592$	$1$	592.bt	148.o	$18$	$6$	$1$	$0.295$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-3$	$0$	$1$		$q+(-\zeta_{18}^{2}-\zeta_{18}^{3})q^{5}+\zeta_{18}^{8}q^{9}+\cdots$
684.1.bx.a	$684$	$1$	684.bx	19.f	$18$	$6$	$1$	$0.341$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{5}+\zeta_{18}^{7})q^{7}+(\zeta_{18}^{3}+\zeta_{18}^{4}+\cdots)q^{13}+\cdots$
740.1.bu.a	$740$	$1$	740.bu	740.au	$18$	$6$	$1$	$0.369$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{8}q^{2}-\zeta_{18}^{7}q^{4}-\zeta_{18}^{5}q^{5}+\cdots$
740.1.bu.b	$740$	$1$	740.bu	740.au	$18$	$6$	$1$	$0.369$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$3$	$0$	$1$		$q-\zeta_{18}^{8}q^{2}-\zeta_{18}^{7}q^{4}+\zeta_{18}^{3}q^{5}+\cdots$
741.1.cm.a	$741$	$1$	741.cm	741.bm	$18$	$6$	$1$	$0.370$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{8}q^{3}-\zeta_{18}^{4}q^{4}+(\zeta_{18}^{2}+\zeta_{18}^{7}+\cdots)q^{7}+\cdots$
741.1.cv.a	$741$	$1$	741.cv	741.bv	$18$	$6$	$1$	$0.370$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}q^{3}+\zeta_{18}^{5}q^{4}+(\zeta_{18}^{2}-\zeta_{18}^{4}+\cdots)q^{7}+\cdots$
763.1.bm.a	$763$	$1$	763.bm	763.am	$18$	$6$	$1$	$0.381$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{2}-\zeta_{18}^{4})q^{2}+(\zeta_{18}^{4}-\zeta_{18}^{6}+\cdots)q^{4}+\cdots$
777.1.cn.a	$777$	$1$	777.cn	777.bn	$18$	$6$	$1$	$0.388$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{2}q^{3}+\zeta_{18}^{5}q^{4}-\zeta_{18}^{4}q^{7}+\cdots$
777.1.ct.a	$777$	$1$	777.ct	777.bt	$18$	$6$	$1$	$0.388$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-6$	$1$		$q+\zeta_{18}^{4}q^{3}+\zeta_{18}q^{4}-q^{7}+\zeta_{18}^{8}q^{9}+\cdots$
828.1.j.a	$828$	$1$	828.j	828.j	$6$	$6$	$3$	$0.413$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{4}q^{2}+\zeta_{18}q^{3}+\zeta_{18}^{8}q^{4}+\zeta_{18}^{5}q^{6}+\cdots$
828.1.j.b	$828$	$1$	828.j	828.j	$6$	$6$	$3$	$0.413$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{2}q^{2}-\zeta_{18}q^{3}+\zeta_{18}^{4}q^{4}+\zeta_{18}^{3}q^{6}+\cdots$
855.1.cw.a	$855$	$1$	855.cw	95.o	$18$	$12$	$2$	$0.427$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{36}^{7}+\zeta_{36}^{15})q^{2}+(\zeta_{36}^{4}-\zeta_{36}^{12}+\cdots)q^{4}+\cdots$
868.1.bj.a	$868$	$1$	868.bj	868.aj	$6$	$6$	$3$	$0.433$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{7}q^{2}-\zeta_{18}^{5}q^{4}+(\zeta_{18}^{2}-\zeta_{18}^{4}+\cdots)q^{5}+\cdots$
868.1.bj.b	$868$	$1$	868.bj	868.aj	$6$	$6$	$3$	$0.433$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{2}q^{2}+\zeta_{18}^{4}q^{4}+(\zeta_{18}-\zeta_{18}^{5}+\cdots)q^{5}+\cdots$
876.1.bh.a	$876$	$1$	876.bh	219.r	$18$	$6$	$1$	$0.437$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$3$	$0$	$0$	$1$		$q+\zeta_{18}^{3}q^{3}+(\zeta_{18}-\zeta_{18}^{5})q^{7}+\zeta_{18}^{6}q^{9}+\cdots$
912.1.ce.a	$912$	$1$	912.ce	228.u	$18$	$6$	$1$	$0.455$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{8}q^{3}+(\zeta_{18}^{2}-\zeta_{18}^{4})q^{7}-\zeta_{18}^{7}q^{9}+\cdots$
912.1.ce.b	$912$	$1$	912.ce	228.u	$18$	$6$	$1$	$0.455$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{8}q^{3}+(-\zeta_{18}^{2}+\zeta_{18}^{4})q^{7}+\cdots$
959.1.d.g	$959$	$1$	959.d	959.d	$2$	$6$	$6$	$0.479$	$\Q(\zeta_{36})^+$	$D_{18}$	$\Q(\sqrt{-959}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$-6$	$1$		$q-\beta _{4}q^{2}-\beta _{1}q^{3}+(1-\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
995.1.c.d	$995$	$1$	995.c	995.c	$2$	$6$	$6$	$0.497$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-199}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}-\zeta_{18}^{8})q^{2}+(-1+\zeta_{18}^{2}+\cdots)q^{4}+\cdots$
995.1.p.a	$995$	$1$	995.p	995.p	$18$	$6$	$1$	$0.497$	$\Q(\zeta_{18})$	$D_{18}$	None	$\Q(\sqrt{5}) $		$4$	$0$	$0$	$0$	$-3$	$0$	$1$		$q-\zeta_{18}^{5}q^{4}-\zeta_{18}^{3}q^{5}-\zeta_{18}^{2}q^{9}+\cdots$
999.1.ce.a	$999$	$1$	999.ce	111.n	$18$	$6$	$1$	$0.499$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-6$	$1$		$q+\zeta_{18}^{5}q^{4}+(-1+\zeta_{18}^{7})q^{7}+(\zeta_{18}^{4}+\cdots)q^{13}+\cdots$
1055.1.d.h	$1055$	$1$	1055.d	1055.d	$2$	$6$	$6$	$0.527$	$\Q(\zeta_{36})^+$	$D_{18}$	$\Q(\sqrt{-1055}) $	None	✓	$4$	$0$	$0$	$0$	$-6$	$0$	$1$		$q+\beta _{3}q^{2}-\beta _{1}q^{3}+2q^{4}-q^{5}+(-2\beta _{2}+\cdots)q^{6}+\cdots$
1064.1.ef.c	$1064$	$1$	1064.ef	1064.df	$18$	$12$	$2$	$0.531$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$0$	$0$	$0$	$6$	$1$		$q+\zeta_{36}^{10}q^{2}+(-\zeta_{36}-\zeta_{36}^{7})q^{3}+\cdots$
1085.1.bh.a	$1085$	$1$	1085.bh	1085.ah	$6$	$6$	$3$	$0.541$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}+\zeta_{18}^{2})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{3}+\cdots)q^{4}+\cdots$
1085.1.bh.b	$1085$	$1$	1085.bh	1085.ah	$6$	$6$	$3$	$0.541$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}-\zeta_{18}^{8})q^{2}+(\zeta_{18}^{3}-\zeta_{18}^{7}+\cdots)q^{4}+\cdots$
1140.1.bx.a	$1140$	$1$	1140.bx	1140.ax	$18$	$6$	$1$	$0.569$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{3}q^{2}-\zeta_{18}^{4}q^{3}+\zeta_{18}^{6}q^{4}+\cdots$
1140.1.bx.b	$1140$	$1$	1140.bx	1140.ax	$18$	$6$	$1$	$0.569$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{8}q^{2}-\zeta_{18}^{4}q^{3}-\zeta_{18}^{7}q^{4}+\cdots$
1140.1.bx.c	$1140$	$1$	1140.bx	1140.ax	$18$	$6$	$1$	$0.569$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{8}q^{2}+\zeta_{18}^{4}q^{3}-\zeta_{18}^{7}q^{4}+\cdots$
1140.1.bx.d	$1140$	$1$	1140.bx	1140.ax	$18$	$6$	$1$	$0.569$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{3}q^{2}+\zeta_{18}^{4}q^{3}+\zeta_{18}^{6}q^{4}+\cdots$
1180.1.b.a	$1180$	$1$	1180.b	295.d	$2$	$6$	$6$	$0.589$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}-\zeta_{18}^{8})q^{3}-\zeta_{18}^{5}q^{5}+(-\zeta_{18}^{2}+\cdots)q^{7}+\cdots$
1197.1.ex.a	$1197$	$1$	1197.ex	133.x	$18$	$6$	$1$	$0.597$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}q^{4}+\zeta_{18}^{7}q^{7}+(\zeta_{18}^{3}+\zeta_{18}^{8}+\cdots)q^{13}+\cdots$
1197.1.fp.a	$1197$	$1$	1197.fp	133.z	$18$	$6$	$1$	$0.597$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{7}q^{4}-\zeta_{18}^{8}q^{7}+(-\zeta_{18}^{3}-\zeta_{18}^{8}+\cdots)q^{13}+\cdots$
1197.1.gi.a	$1197$	$1$	1197.gi	133.ad	$18$	$6$	$1$	$0.597$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}q^{4}+\zeta_{18}^{7}q^{7}+(\zeta_{18}^{3}+\zeta_{18}^{8}+\cdots)q^{13}+\cdots$
1197.1.hb.a	$1197$	$1$	1197.hb	133.ae	$18$	$6$	$1$	$0.597$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{7}q^{4}-\zeta_{18}^{8}q^{7}+(\zeta_{18}^{3}+\zeta_{18}^{8}+\cdots)q^{13}+\cdots$
1216.1.bi.a	$1216$	$1$	1216.bi	152.s	$18$	$12$	$2$	$0.607$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{36}^{13}+\zeta_{36}^{15})q^{3}+(-\zeta_{36}^{8}-\zeta_{36}^{10}+\cdots)q^{9}+\cdots$
1299.1.t.a	$1299$	$1$	1299.t	1299.t	$18$	$6$	$1$	$0.648$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{4}q^{3}-\zeta_{18}^{3}q^{4}+(-\zeta_{18}^{2}+\zeta_{18}^{8}+\cdots)q^{7}+\cdots$
1332.1.cy.a	$1332$	$1$	1332.cy	148.o	$18$	$12$	$2$	$0.665$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{36}^{13}q^{2}-\zeta_{36}^{8}q^{4}+(-\zeta_{36}^{7}+\cdots)q^{5}+\cdots$
1368.1.dk.a	$1368$	$1$	1368.dk	1368.ck	$18$	$6$	$1$	$0.683$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}q^{2}+\zeta_{18}^{2}q^{3}+\zeta_{18}^{2}q^{4}+\zeta_{18}^{3}q^{6}+\cdots$

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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.