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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 536 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
136.1.p.a	$136$	$1$	136.p	136.p	$8$	$4$	$1$	$0.068$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}^{3}q^{2}+(\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots$
224.1.v.a	$224$	$1$	224.v	224.v	$8$	$4$	$1$	$0.112$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}q^{7}+\zeta_{8}^{3}q^{8}+\cdots$
255.1.y.a	$255$	$1$	255.y	255.y	$8$	$8$	$2$	$0.127$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{16}-\zeta_{16}^{3})q^{2}-\zeta_{16}^{7}q^{3}+(\zeta_{16}^{2}+\cdots)q^{4}+\cdots$
272.1.u.a	$272$	$1$	272.u	68.g	$8$	$4$	$1$	$0.136$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}+\zeta_{8}q^{9}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{13}+\cdots$
291.1.k.a	$291$	$1$	291.k	291.k	$8$	$4$	$1$	$0.145$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-4$	$1$		$q-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}+(-1-\zeta_{8}^{3})q^{7}+\cdots$
323.1.l.a	$323$	$1$	323.l	323.l	$8$	$4$	$1$	$0.161$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-4$	$0$	$1$		$q+\zeta_{8}^{2}q^{4}+(-1-\zeta_{8}^{3})q^{5}+(\zeta_{8}^{2}+\zeta_{8}^{3}+\cdots)q^{7}+\cdots$
328.1.n.a	$328$	$1$	328.n	328.n	$8$	$4$	$1$	$0.164$	$\Q(\zeta_{8})$	$D_{8}$	None	$\Q(\sqrt{2}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\zeta_{8}^{2})q^{7}+\cdots$
340.1.ba.a	$340$	$1$	340.ba	340.aa	$8$	$4$	$1$	$0.170$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{2}q^{5}-\zeta_{8}^{3}q^{8}+\cdots$
340.1.ba.b	$340$	$1$	340.ba	340.aa	$8$	$4$	$1$	$0.170$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\zeta_{8}^{3}q^{8}+\cdots$
388.1.k.a	$388$	$1$	388.k	388.k	$8$	$4$	$1$	$0.194$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-4$	$0$	$1$		$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-1+\zeta_{8})q^{5}+\cdots$
407.1.d.c	$407$	$1$	407.d	407.d	$2$	$4$	$4$	$0.203$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-407}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}-\beta _{2}q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots$
471.1.d.c	$471$	$1$	471.d	471.d	$2$	$4$	$4$	$0.235$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-471}) $	None	✓	$4$	$0$	$0$	$-4$	$0$	$0$	$1$		$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots$
480.1.bu.a	$480$	$1$	480.bu	480.au	$8$	$8$	$2$	$0.240$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}^{3}q^{2}-\zeta_{16}^{7}q^{3}+\zeta_{16}^{6}q^{4}+\cdots$
544.1.bl.a	$544$	$1$	544.bl	136.p	$8$	$4$	$1$	$0.271$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-1-\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{9}+\cdots$
555.1.b.a	$555$	$1$	555.b	555.b	$2$	$8$	$8$	$0.277$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{16}-\zeta_{16}^{7})q^{2}+\zeta_{16}^{4}q^{3}+(-1+\cdots)q^{4}+\cdots$
559.1.d.c	$559$	$1$	559.d	559.d	$2$	$4$	$4$	$0.279$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-559}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\beta _{1}q^{7}+\cdots$
579.1.l.a	$579$	$1$	579.l	579.l	$8$	$4$	$1$	$0.289$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}^{2}q^{3}+\zeta_{8}^{2}q^{4}+(\zeta_{8}-\zeta_{8}^{3})q^{7}+\cdots$
584.1.h.c	$584$	$1$	584.h	584.h	$2$	$4$	$4$	$0.291$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-146}) $	None	✓	$4$	$0$	$-4$	$0$	$0$	$0$	$1$		$q-q^{2}-\beta _{2}q^{3}+q^{4}-\beta _{1}q^{5}+\beta _{2}q^{6}+\cdots$
585.1.o.a	$585$	$1$	585.o	65.h	$4$	$8$	$4$	$0.292$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{16}^{5}-\zeta_{16}^{7})q^{2}+(-\zeta_{16}^{2}+\zeta_{16}^{4}+\cdots)q^{4}+\cdots$
595.1.be.a	$595$	$1$	595.be	595.ae	$8$	$8$	$2$	$0.297$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-35}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{16}-\zeta_{16}^{5})q^{3}+\zeta_{16}^{4}q^{4}-\zeta_{16}^{3}q^{5}+\cdots$
612.1.v.a	$612$	$1$	612.v	68.g	$8$	$4$	$1$	$0.305$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-4$	$0$	$1$		$q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(-1+\zeta_{8})q^{5}+\cdots$
612.1.v.b	$612$	$1$	612.v	68.g	$8$	$4$	$1$	$0.305$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$4$	$0$	$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(1-\zeta_{8})q^{5}-\zeta_{8}q^{8}+\cdots$
624.1.bi.a	$624$	$1$	624.bi	624.ai	$4$	$8$	$4$	$0.311$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}^{3}q^{2}-\zeta_{16}^{2}q^{3}+\zeta_{16}^{6}q^{4}+\cdots$
656.1.h.a	$656$	$1$	656.h	164.d	$2$	$4$	$4$	$0.327$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-41}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{3}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots$
657.1.x.a	$657$	$1$	657.x	73.f	$8$	$4$	$1$	$0.328$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}+(\zeta_{8}^{2}-\zeta_{8}^{3})q^{7}+(\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{13}+\cdots$
723.1.m.a	$723$	$1$	723.m	723.m	$8$	$4$	$1$	$0.361$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+(\zeta_{8}-\zeta_{8}^{2})q^{7}+\cdots$
731.1.l.a	$731$	$1$	731.l	731.l	$8$	$4$	$1$	$0.365$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-43}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{9}+(-\zeta_{8}-\zeta_{8}^{2})q^{11}+\cdots$
736.1.p.a	$736$	$1$	736.p	736.p	$8$	$4$	$1$	$0.367$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$-4$	$0$	$0$	$1$		$q+\zeta_{8}q^{2}+(-1+\zeta_{8})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
760.1.b.a	$760$	$1$	760.b	760.b	$2$	$8$	$8$	$0.379$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{16}q^{2}+(\zeta_{16}^{3}+\zeta_{16}^{5})q^{3}+\zeta_{16}^{2}q^{4}+\cdots$
772.1.l.a	$772$	$1$	772.l	772.l	$8$	$4$	$1$	$0.385$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}+\cdots$
776.1.x.a	$776$	$1$	776.x	776.x	$8$	$4$	$1$	$0.387$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$4$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+(1-\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{6}+\cdots$
780.1.w.a	$780$	$1$	780.w	780.w	$4$	$8$	$4$	$0.389$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}^{3}q^{2}+\zeta_{16}^{2}q^{3}+\zeta_{16}^{6}q^{4}+\cdots$
780.1.w.b	$780$	$1$	780.w	780.w	$4$	$8$	$4$	$0.389$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}^{5}q^{2}+\zeta_{16}^{2}q^{3}-\zeta_{16}^{2}q^{4}+\cdots$
791.1.d.c	$791$	$1$	791.d	791.d	$2$	$4$	$4$	$0.395$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-791}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$4$	$1$		$q-\beta _{2}q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{5}+(\beta _{1}+\cdots)q^{6}+\cdots$
791.1.l.a	$791$	$1$	791.l	791.l	$8$	$4$	$1$	$0.395$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$4$	$1$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}-q^{4}+q^{7}+\zeta_{8}^{3}q^{9}+\cdots$
799.1.c.c	$799$	$1$	799.c	799.c	$2$	$4$	$4$	$0.399$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-799}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{2}q^{2}+q^{4}-\beta _{1}q^{5}+q^{9}+(\beta _{1}+\beta _{3})q^{10}+\cdots$
799.1.h.a	$799$	$1$	799.h	799.h	$8$	$4$	$1$	$0.399$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$0$	$4$	$0$	$0$	$1$		$q+(1-\zeta_{8})q^{3}+\zeta_{8}^{2}q^{4}+(\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{7}+\cdots$
820.1.e.c	$820$	$1$	820.e	820.e	$2$	$8$	$8$	$0.409$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-41}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2$		$q+\zeta_{16}^{4}q^{2}+(-\zeta_{16}-\zeta_{16}^{7})q^{3}-q^{4}+\cdots$
820.1.z.a	$820$	$1$	820.z	820.z	$8$	$4$	$1$	$0.409$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-4$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-\zeta_{8}^{3}q^{5}-q^{8}+\zeta_{8}q^{9}+\cdots$
820.1.ba.a	$820$	$1$	820.ba	820.aa	$8$	$4$	$1$	$0.409$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{2}q^{2}-q^{4}+\zeta_{8}^{3}q^{5}+\zeta_{8}^{2}q^{8}+\cdots$
840.1.bp.c	$840$	$1$	840.bp	840.ap	$4$	$8$	$4$	$0.419$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{16}^{2}q^{2}+\zeta_{16}^{5}q^{3}+\zeta_{16}^{4}q^{4}+\cdots$
840.1.bp.d	$840$	$1$	840.bp	840.ap	$4$	$8$	$4$	$0.419$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{16}^{2}q^{2}+\zeta_{16}^{3}q^{3}+\zeta_{16}^{4}q^{4}+\cdots$
880.1.x.a	$880$	$1$	880.x	880.x	$4$	$8$	$4$	$0.439$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}+\zeta_{16}^{6}q^{5}+\cdots$
884.1.bg.a	$884$	$1$	884.bg	884.ag	$8$	$4$	$1$	$0.441$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}+\cdots$
884.1.bg.b	$884$	$1$	884.bg	884.ag	$8$	$4$	$1$	$0.441$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}^{2}-\zeta_{8}^{3}+\cdots)q^{5}+\cdots$
884.1.bg.c	$884$	$1$	884.bg	884.ag	$8$	$4$	$1$	$0.441$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(\zeta_{8}-\zeta_{8}^{2})q^{7}+\cdots$
884.1.bg.d	$884$	$1$	884.bg	884.ag	$8$	$4$	$1$	$0.441$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{7}+\cdots$
888.1.i.e	$888$	$1$	888.i	888.i	$2$	$8$	$8$	$0.443$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-111}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{16}q^{2}-\zeta_{16}^{4}q^{3}+\zeta_{16}^{2}q^{4}+(\zeta_{16}^{3}+\cdots)q^{5}+\cdots$
895.1.d.d	$895$	$1$	895.d	895.d	$2$	$4$	$4$	$0.447$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-895}) $	None	✓	$4$	$0$	$0$	$0$	$-4$	$0$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{3}q^{7}+\cdots$
896.1.v.a	$896$	$1$	896.v	224.v	$8$	$4$	$1$	$0.447$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{3}q^{7}-\zeta_{8}q^{9}+(-\zeta_{8}-\zeta_{8}^{2})q^{11}+\cdots$

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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.