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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 733 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
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		$4$	$0$	$0$	$-3$	$0$	$0$	$1$		$q-\zeta_{18}^{5}q^{2}+(\zeta_{18}^{6}-\zeta_{18}^{7})q^{3}-\zeta_{18}q^{4}+\cdots$
199.1.b.b	$199$	$1$	199.b	199.b	$2$	$3$	$3$	$0.099$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-199}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$-3$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots$
207.1.f.a	$207$	$1$	207.f	207.f	$6$	$6$	$3$	$0.103$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{2}+\zeta_{18}^{2}q^{3}+(-\zeta_{18}^{3}+\cdots)q^{4}+\cdots$
216.1.r.a	$216$	$1$	216.r	216.r	$18$	$6$	$1$	$0.108$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{2}q^{2}+\zeta_{18}^{8}q^{3}+\zeta_{18}^{4}q^{4}+\cdots$
217.1.n.a	$217$	$1$	217.n	217.n	$6$	$6$	$3$	$0.108$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}-\zeta_{18}^{5})q^{2}+(-\zeta_{18}+\zeta_{18}^{2}+\cdots)q^{4}+\cdots$
228.1.s.a	$228$	$1$	228.s	57.l	$18$	$6$	$1$	$0.114$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{8}q^{3}+(\zeta_{18}^{2}+\zeta_{18}^{4})q^{7}-\zeta_{18}^{7}q^{9}+\cdots$
236.1.d.a	$236$	$1$	236.d	59.b	$2$	$3$	$3$	$0.118$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-59}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{7}+(1+\cdots)q^{9}+\cdots$
259.1.bi.a	$259$	$1$	259.bi	259.ai	$18$	$6$	$1$	$0.129$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}^{3}+\zeta_{18}^{4})q^{2}+(\zeta_{18}^{6}-\zeta_{18}^{7}+\cdots)q^{4}+\cdots$
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		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}^{4}-\zeta_{18}^{6})q^{2}-\zeta_{18}^{2}q^{3}+\cdots$
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		$4$	$0$	$0$	$0$	$-3$	$0$	$1$		$q+\zeta_{18}^{8}q^{3}+\zeta_{18}^{2}q^{4}+(-\zeta_{18}^{3}-\zeta_{18}^{7}+\cdots)q^{5}+\cdots$
299.1.h.a	$299$	$1$	299.h	299.h	$6$	$6$	$3$	$0.149$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}-\zeta_{18}^{5})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{4}+\cdots)q^{3}+\cdots$
327.1.o.a	$327$	$1$	327.o	327.o	$18$	$6$	$1$	$0.163$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-3$	$1$		$q+\zeta_{18}^{4}q^{3}+\zeta_{18}^{6}q^{4}+(-\zeta_{18}^{5}+\zeta_{18}^{6}+\cdots)q^{7}+\cdots$
332.1.d.a	$332$	$1$	332.d	83.b	$2$	$3$	$3$	$0.166$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-83}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{7}+(1+\beta _{2})q^{9}+\cdots$
335.1.d.c	$335$	$1$	335.d	335.d	$2$	$3$	$3$	$0.167$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-335}) $	None	✓	$2$	$0$	$0$	$0$	$-3$	$0$	$1$		$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots$
335.1.d.d	$335$	$1$	335.d	335.d	$2$	$3$	$3$	$0.167$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-335}) $	None	✓	$2$	$0$	$0$	$0$	$3$	$0$	$1$		$q-\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots$
367.1.b.b	$367$	$1$	367.b	367.b	$2$	$3$	$3$	$0.183$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-367}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{7}+\cdots$
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		$4$	$0$	$0$	$-3$	$0$	$0$	$1$		$q+(\zeta_{18}^{2}+\zeta_{18}^{6})q^{3}-\zeta_{18}q^{4}+\zeta_{18}^{7}q^{5}+\cdots$
419.1.b.b	$419$	$1$	419.b	419.b	$2$	$3$	$3$	$0.209$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-419}) $	None	✓	$2$	$0$	$0$	$0$	$-3$	$0$	$1$		$q-\beta _{1}q^{3}+q^{4}-q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots$
428.1.d.a	$428$	$1$	428.d	107.b	$2$	$3$	$3$	$0.214$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-107}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{3}+(1+\beta _{2})q^{9}+(\beta _{1}-\beta _{2})q^{11}+\cdots$
436.1.n.a	$436$	$1$	436.n	436.n	$18$	$6$	$1$	$0.218$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{3}q^{2}+\zeta_{18}^{6}q^{4}+\zeta_{18}q^{5}+q^{8}+\cdots$
444.1.bf.a	$444$	$1$	444.bf	111.p	$18$	$6$	$1$	$0.222$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-3$	$1$		$q+\zeta_{18}^{8}q^{3}+(-\zeta_{18}^{3}-\zeta_{18}^{7})q^{7}+\cdots$
489.1.k.a	$489$	$1$	489.k	489.k	$18$	$6$	$1$	$0.244$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-3$	$1$		$q-\zeta_{18}^{7}q^{3}-\zeta_{18}^{7}q^{4}+(-\zeta_{18}+\zeta_{18}^{6}+\cdots)q^{7}+\cdots$
491.1.b.c	$491$	$1$	491.b	491.b	$2$	$3$	$3$	$0.245$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-491}) $	None	✓	$2$	$0$	$0$	$0$	$-3$	$0$	$1$		$q-\beta _{1}q^{3}+q^{4}-q^{5}+(1+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots$
513.1.bs.a	$513$	$1$	513.bs	57.l	$18$	$6$	$1$	$0.256$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{4}q^{4}+(-\zeta_{18}^{7}+\zeta_{18}^{8})q^{7}+\cdots$
519.1.d.c	$519$	$1$	519.d	519.d	$2$	$3$	$3$	$0.259$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-519}) $	None	✓	$2$	$0$	$0$	$-3$	$0$	$0$	$1$		$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
519.1.d.d	$519$	$1$	519.d	519.d	$2$	$3$	$3$	$0.259$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-519}) $	None	✓	$2$	$0$	$0$	$3$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots$
527.1.d.c	$527$	$1$	527.d	527.d	$2$	$3$	$3$	$0.263$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-527}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\beta _{1}-\beta _{2})q^{2}-\beta _{1}q^{3}+(1-\beta _{1})q^{4}+\cdots$
527.1.d.d	$527$	$1$	527.d	527.d	$2$	$3$	$3$	$0.263$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-527}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\beta _{1}-\beta _{2})q^{2}+\beta _{1}q^{3}+(1-\beta _{1})q^{4}+\cdots$
531.1.g.a	$531$	$1$	531.g	531.g	$6$	$6$	$3$	$0.265$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{8}q^{3}+\zeta_{18}^{6}q^{4}+(\zeta_{18}^{4}+\zeta_{18}^{8}+\cdots)q^{5}+\cdots$
540.1.bf.a	$540$	$1$	540.bf	540.af	$18$	$6$	$1$	$0.269$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$0$	$0$	$-3$	$1$		$q-\zeta_{18}q^{2}-\zeta_{18}^{5}q^{3}+\zeta_{18}^{2}q^{4}-\zeta_{18}^{5}q^{5}+\cdots$
540.1.bf.b	$540$	$1$	540.bf	540.af	$18$	$6$	$1$	$0.269$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$0$	$0$	$3$	$1$		$q+\zeta_{18}q^{2}+\zeta_{18}^{5}q^{3}+\zeta_{18}^{2}q^{4}-\zeta_{18}^{5}q^{5}+\cdots$
556.1.c.a	$556$	$1$	556.c	139.b	$2$	$3$	$3$	$0.277$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-139}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{5}+\beta _{2}q^{7}+q^{9}+(\beta _{1}-\beta _{2})q^{11}+\cdots$
563.1.b.c	$563$	$1$	563.b	563.b	$2$	$3$	$3$	$0.281$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-563}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{7}+(1+\beta _{2})q^{9}+\cdots$
575.1.c.b	$575$	$1$	575.c	115.c	$2$	$6$	$6$	$0.287$	6.0.419904.1	$D_{9}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+(-\beta _{1}-\beta _{5})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$
575.1.d.b	$575$	$1$	575.d	23.b	$2$	$3$	$3$	$0.287$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-23}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+\beta _{2}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots$
575.1.d.c	$575$	$1$	575.d	23.b	$2$	$3$	$3$	$0.287$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-23}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots$
581.1.g.b	$581$	$1$	581.g	581.g	$6$	$6$	$3$	$0.290$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}-\zeta_{18}^{5})q^{3}-\zeta_{18}^{3}q^{4}+\zeta_{18}^{8}q^{7}+\cdots$
584.1.be.a	$584$	$1$	584.be	584.ae	$18$	$6$	$1$	$0.291$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{8}q^{2}+(-\zeta_{18}+\zeta_{18}^{2})q^{3}-\zeta_{18}^{7}q^{4}+\cdots$
589.1.m.a	$589$	$1$	589.m	589.m	$6$	$6$	$3$	$0.294$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}-\zeta_{18}^{5})q^{2}+(-\zeta_{18}+\zeta_{18}^{2}+\cdots)q^{4}+\cdots$
608.1.bg.a	$608$	$1$	608.bg	152.u	$18$	$6$	$1$	$0.303$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$3$	$0$	$0$	$1$		$q+(\zeta_{18}-\zeta_{18}^{6})q^{3}+(\zeta_{18}^{2}-\zeta_{18}^{3}+\cdots)q^{9}+\cdots$
609.1.p.a	$609$	$1$	609.p	609.p	$6$	$6$	$3$	$0.304$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$0$	$-3$	$0$	$0$	$1$		$q+(-\zeta_{18}-\zeta_{18}^{5})q^{2}+\zeta_{18}^{6}q^{3}+(-\zeta_{18}+\cdots)q^{4}+\cdots$
609.1.p.b	$609$	$1$	609.p	609.p	$6$	$6$	$3$	$0.304$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$0$	$3$	$0$	$0$	$1$		$q+(-\zeta_{18}^{2}-\zeta_{18}^{4})q^{2}-\zeta_{18}^{6}q^{3}+\cdots$
621.1.f.a	$621$	$1$	621.f	207.f	$6$	$6$	$3$	$0.310$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$3$		$q+(\zeta_{18}-\zeta_{18}^{2})q^{2}+(\zeta_{18}^{2}-\zeta_{18}^{3}+\cdots)q^{4}+\cdots$
648.1.r.a	$648$	$1$	648.r	216.r	$18$	$6$	$1$	$0.323$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+\zeta_{18}^{3}q^{8}+\cdots$
679.1.c.c	$679$	$1$	679.c	679.c	$2$	$3$	$3$	$0.339$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-679}) $	None	✓	$2$	$0$	$0$	$0$	$-3$	$3$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+q^{7}+(-1+\cdots)q^{8}+\cdots$

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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.