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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 57083 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
417.1.l.a	$417$	$1$	417.l	417.l	$46$	$22$	$1$	$0.208$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{46}^{21}q^{3}+\zeta_{46}^{10}q^{4}+(-\zeta_{46}+\cdots)q^{7}+\cdots$
472.1.k.a	$472$	$1$	472.k	472.k	$58$	$28$	$1$	$0.236$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q+\zeta_{58}^{4}q^{2}+(-\zeta_{58}^{5}+\zeta_{58}^{18})q^{3}+\cdots$
497.1.ba.a	$497$	$1$	497.ba	497.aa	$70$	$24$	$1$	$0.248$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-3$	$0$	$0$	$1$	$1$		$q+(\zeta_{70}^{12}+\zeta_{70}^{20})q^{2}+(-\zeta_{70}^{5}+\zeta_{70}^{24}+\cdots)q^{4}+\cdots$
517.1.k.a	$517$	$1$	517.k	517.k	$46$	$22$	$1$	$0.258$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$-2$	$0$	$1$		$q+(\zeta_{46}^{16}+\zeta_{46}^{20})q^{3}+\zeta_{46}^{14}q^{4}+\cdots$
553.1.bg.a	$553$	$1$	553.bg	553.ag	$78$	$24$	$1$	$0.276$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-1$	$0$	$0$	$1$	$1$		$q+(\zeta_{78}^{16}+\zeta_{78}^{18})q^{2}+(\zeta_{78}^{32}+\zeta_{78}^{34}+\cdots)q^{4}+\cdots$
596.1.j.a	$596$	$1$	596.j	596.j	$74$	$36$	$1$	$0.297$	$\Q(\zeta_{74})$	$D_{37}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q+\zeta_{74}^{24}q^{2}-\zeta_{74}^{11}q^{4}+(\zeta_{74}^{14}+\cdots)q^{5}+\cdots$
628.1.u.a	$628$	$1$	628.u	628.u	$78$	$24$	$1$	$0.313$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$2$	$0$	$1$		$q-\zeta_{78}^{3}q^{2}+\zeta_{78}^{6}q^{4}+(-\zeta_{78}^{17}+\cdots)q^{5}+\cdots$
633.1.z.a	$633$	$1$	633.z	633.z	$70$	$24$	$1$	$0.316$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-3$	$1$		$q-\zeta_{70}^{9}q^{3}-\zeta_{70}^{11}q^{4}+(-\zeta_{70}^{5}+\cdots)q^{7}+\cdots$
649.1.l.a	$649$	$1$	649.l	649.l	$58$	$28$	$1$	$0.324$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$-2$	$0$	$1$		$q+(\zeta_{58}^{8}-\zeta_{58}^{11})q^{3}-\zeta_{58}^{23}q^{4}+\cdots$
41.2.g.a	$41$	$2$	41.g	41.g	$20$	$24$	$3$	$0.327$		$_{}$	None	None		$2$	$0$	$-10$	$-6$	$-10$	$-8$		$\mathrm{SU}(2)[C_{20}]$
664.1.l.a	$664$	$1$	664.l	664.l	$82$	$40$	$1$	$0.331$	$\Q(\zeta_{82})$	$D_{41}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q+\zeta_{82}^{32}q^{2}+(\zeta_{82}^{28}-\zeta_{82}^{29})q^{3}+\cdots$
669.1.l.a	$669$	$1$	669.l	669.l	$74$	$36$	$1$	$0.334$	$\Q(\zeta_{74})$	$D_{37}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{74}^{31}q^{3}-\zeta_{74}^{23}q^{4}+(-\zeta_{74}^{7}+\cdots)q^{7}+\cdots$
676.1.t.a	$676$	$1$	676.t	676.t	$78$	$24$	$1$	$0.337$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$2$	$0$	$1$		$q+\zeta_{78}^{8}q^{2}+\zeta_{78}^{16}q^{4}+(\zeta_{78}^{28}+\zeta_{78}^{38}+\cdots)q^{5}+\cdots$
43.2.g.a	$43$	$2$	43.g	43.g	$21$	$36$	$3$	$0.343$		$_{}$	None	None		$2$	$0$	$-10$	$-16$	$-17$	$6$		$\mathrm{SU}(2)[C_{21}]$
692.1.i.a	$692$	$1$	692.i	692.i	$86$	$42$	$1$	$0.345$	$\Q(\zeta_{86})$	$D_{43}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{86}^{11}q^{2}+\zeta_{86}^{22}q^{4}+(-\zeta_{86}^{5}+\cdots)q^{5}+\cdots$
705.1.p.a	$705$	$1$	705.p	705.p	$46$	$22$	$1$	$0.352$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-2$	$-1$	$-1$	$0$	$1$		$q+(\zeta_{46}^{4}+\zeta_{46}^{6})q^{2}-\zeta_{46}^{3}q^{3}+(\zeta_{46}^{8}+\cdots)q^{4}+\cdots$
705.1.p.b	$705$	$1$	705.p	705.p	$46$	$22$	$1$	$0.352$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$2$	$1$	$1$	$0$	$1$		$q+(-\zeta_{46}^{4}-\zeta_{46}^{6})q^{2}+\zeta_{46}^{3}q^{3}+\cdots$
713.1.t.a	$713$	$1$	713.t	713.t	$30$	$24$	$3$	$0.356$	$\Q(\zeta_{45})$	$D_{45}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{90}^{25}-\zeta_{90}^{29})q^{2}+(\zeta_{90}^{2}-\zeta_{90}^{19}+\cdots)q^{3}+\cdots$
724.1.bg.a	$724$	$1$	724.bg	724.ag	$90$	$24$	$1$	$0.361$	$\Q(\zeta_{45})$	$D_{45}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{90}^{23}q^{2}-\zeta_{90}q^{4}+(\zeta_{90}^{26}+\zeta_{90}^{40}+\cdots)q^{5}+\cdots$
749.1.j.a	$749$	$1$	749.j	749.j	$106$	$52$	$1$	$0.374$	$\Q(\zeta_{106})$	$D_{53}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$	$1$		$q+(-\zeta_{106}^{25}+\zeta_{106}^{40})q^{2}+(\zeta_{106}^{12}+\cdots)q^{4}+\cdots$
47.2.c.a	$47$	$2$	47.c	47.c	$23$	$66$	$3$	$0.375$		$_{}$	None	None		$2$	$0$	$-21$	$-19$	$-15$	$-19$		$\mathrm{SU}(2)[C_{23}]$
781.1.bp.a	$781$	$1$	781.bp	781.ap	$70$	$24$	$1$	$0.390$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-5$	$2$	$0$	$1$		$q+(\zeta_{70}^{8}+\zeta_{70}^{14})q^{3}+\zeta_{70}^{32}q^{4}+\cdots$
49.2.g.a	$49$	$2$	49.g	49.g	$21$	$48$	$4$	$0.391$		$_{}$	None	None		$2$	$0$	$-13$	$-14$	$-14$	$-14$		$\mathrm{SU}(2)[C_{21}]$
788.1.o.a	$788$	$1$	788.o	788.o	$98$	$42$	$1$	$0.393$	$\Q(\zeta_{98})$	$D_{49}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{98}^{43}q^{2}-\zeta_{98}^{37}q^{4}+(-\zeta_{98}+\cdots)q^{5}+\cdots$
791.1.bf.a	$791$	$1$	791.bf	791.af	$56$	$24$	$1$	$0.395$	$\Q(\zeta_{56})$	$D_{56}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$-4$	$1$		$q+(-\zeta_{56}^{21}+\zeta_{56}^{27})q^{2}+(-\zeta_{56}^{14}+\cdots)q^{4}+\cdots$
795.1.bb.a	$795$	$1$	795.bb	795.ab	$26$	$24$	$2$	$0.397$	$\Q(\zeta_{52})$	$D_{26}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{52}^{9}-\zeta_{52}^{11})q^{2}+\zeta_{52}q^{3}+(\zeta_{52}^{18}+\cdots)q^{4}+\cdots$
813.1.z.a	$813$	$1$	813.z	813.z	$90$	$24$	$1$	$0.406$	$\Q(\zeta_{45})$	$D_{45}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-6$	$0$	$3$	$1$		$q+\zeta_{90}^{36}q^{3}+\zeta_{90}^{4}q^{4}+(-\zeta_{90}^{3}+\cdots)q^{7}+\cdots$
51.2.i.a	$51$	$2$	51.i	51.i	$16$	$32$	$4$	$0.407$		$_{}$	None	None		$4$	$0$	$0$	$-8$	$0$	$-16$		$\mathrm{SU}(2)[C_{16}]$
831.1.n.a	$831$	$1$	831.n	831.n	$46$	$22$	$1$	$0.415$	$\Q(\zeta_{46})$	$D_{46}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$2$	$1$		$q-\zeta_{46}^{18}q^{3}-\zeta_{46}^{12}q^{4}+(-\zeta_{46}^{16}+\cdots)q^{7}+\cdots$
831.1.p.a	$831$	$1$	831.p	831.p	$46$	$22$	$1$	$0.415$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q+\zeta_{46}^{2}q^{3}-\zeta_{46}^{9}q^{4}+(\zeta_{46}^{10}+\zeta_{46}^{12}+\cdots)q^{7}+\cdots$
847.1.bb.a	$847$	$1$	847.bb	847.ab	$110$	$40$	$1$	$0.423$	$\Q(\zeta_{55})$	$D_{55}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$1$	$1$		$q+(\zeta_{110}^{8}-\zeta_{110}^{49})q^{2}+(\zeta_{110}^{2}+\zeta_{110}^{16}+\cdots)q^{4}+\cdots$
53.2.d.a	$53$	$2$	53.d	53.d	$13$	$36$	$3$	$0.423$		$_{}$	None	None		$2$	$0$	$-8$	$-9$	$-5$	$-5$		$\mathrm{SU}(2)[C_{13}]$
53.2.e.a	$53$	$2$	53.e	53.e	$26$	$48$	$4$	$0.423$		$_{}$	None	None		$2$	$0$	$-13$	$-13$	$-13$	$-5$		$\mathrm{SU}(2)[C_{26}]$
849.1.l.a	$849$	$1$	849.l	849.l	$94$	$46$	$1$	$0.424$	$\Q(\zeta_{94})$	$D_{47}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{94}^{45}q^{3}+\zeta_{94}^{22}q^{4}+(-\zeta_{94}^{29}+\cdots)q^{7}+\cdots$
856.1.l.a	$856$	$1$	856.l	856.l	$106$	$52$	$1$	$0.427$	$\Q(\zeta_{106})$	$D_{53}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q-\zeta_{106}^{9}q^{2}+(\zeta_{106}^{4}-\zeta_{106}^{37})q^{3}+\zeta_{106}^{18}q^{4}+\cdots$
55.2.l.a	$55$	$2$	55.l	55.l	$20$	$32$	$4$	$0.439$		$_{}$	None	None		$4$	$0$	$-10$	$-4$	$-2$	$0$		$\mathrm{SU}(2)[C_{20}]$
889.1.ce.a	$889$	$1$	889.ce	889.be	$126$	$36$	$1$	$0.444$	$\Q(\zeta_{63})$	$D_{63}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{126}^{14}+\zeta_{126}^{58})q^{2}+(-\zeta_{126}^{9}+\zeta_{126}^{28}+\cdots)q^{4}+\cdots$
893.1.o.a	$893$	$1$	893.o	893.o	$46$	$22$	$1$	$0.446$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$-2$	$1$		$q-\zeta_{46}^{19}q^{4}+(\zeta_{46}^{12}-\zeta_{46}^{21})q^{5}+\cdots$
904.1.bi.a	$904$	$1$	904.bi	904.ai	$56$	$24$	$1$	$0.451$	$\Q(\zeta_{56})$	$D_{56}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{56}^{22}q^{2}+(\zeta_{56}^{2}-\zeta_{56}^{25})q^{3}+\cdots$
57.2.j.b	$57$	$2$	57.j	57.j	$18$	$24$	$4$	$0.455$		$_{}$	None	None		$4$	$0$	$0$	$-9$	$0$	$-6$		$\mathrm{SU}(2)[C_{18}]$
916.1.t.a	$916$	$1$	916.t	916.t	$114$	$36$	$1$	$0.457$	$\Q(\zeta_{57})$	$D_{57}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$-1$	$0$	$1$		$q+\zeta_{114}^{24}q^{2}+\zeta_{114}^{48}q^{4}+(-\zeta_{114}^{13}+\cdots)q^{5}+\cdots$
921.1.s.a	$921$	$1$	921.s	921.s	$102$	$32$	$1$	$0.460$	$\Q(\zeta_{51})$	$D_{51}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-2$	$0$	$-15$	$1$		$q-\zeta_{102}^{9}q^{3}-\zeta_{102}^{15}q^{4}+(-\zeta_{102}^{5}+\cdots)q^{7}+\cdots$
932.1.j.a	$932$	$1$	932.j	932.j	$58$	$28$	$1$	$0.465$	$\Q(\zeta_{58})$	$D_{58}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+\zeta_{58}^{13}q^{2}+\zeta_{58}^{26}q^{4}+(\zeta_{58}^{15}+\cdots)q^{5}+\cdots$
932.1.k.a	$932$	$1$	932.k	932.k	$58$	$28$	$1$	$0.465$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{58}^{21}q^{2}-\zeta_{58}^{13}q^{4}+(-\zeta_{58}^{9}+\cdots)q^{5}+\cdots$
939.1.v.a	$939$	$1$	939.v	939.v	$52$	$24$	$1$	$0.469$	$\Q(\zeta_{52})$	$D_{52}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$2$	$0$	$2$	$1$		$q+\zeta_{52}^{14}q^{3}-\zeta_{52}^{20}q^{4}+(-\zeta_{52}^{5}+\cdots)q^{7}+\cdots$
940.1.p.a	$940$	$1$	940.p	940.p	$46$	$22$	$1$	$0.469$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-1$	$-2$	$-1$	$-2$	$1$		$q-\zeta_{46}^{13}q^{2}+(-\zeta_{46}^{5}+\zeta_{46}^{6})q^{3}+\cdots$
940.1.p.b	$940$	$1$	940.p	940.p	$46$	$22$	$1$	$0.469$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$1$	$2$	$-1$	$2$	$1$		$q+\zeta_{46}^{13}q^{2}+(\zeta_{46}^{5}-\zeta_{46}^{6})q^{3}-\zeta_{46}^{3}q^{4}+\cdots$
948.1.bb.a	$948$	$1$	948.bb	237.o	$78$	$24$	$1$	$0.473$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$2$	$1$		$q+\zeta_{78}^{4}q^{3}+(-\zeta_{78}^{5}-\zeta_{78}^{29})q^{7}+\cdots$
959.1.v.a	$959$	$1$	959.v	959.v	$68$	$32$	$1$	$0.479$	$\Q(\zeta_{68})$	$D_{68}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{68}^{2}+\zeta_{68}^{20})q^{2}+(\zeta_{68}^{4}-\zeta_{68}^{6}+\cdots)q^{4}+\cdots$
968.1.z.a	$968$	$1$	968.z	968.z	$110$	$40$	$1$	$0.483$	$\Q(\zeta_{55})$	$D_{55}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$2$	$0$	$0$	$1$		$q-\zeta_{110}^{49}q^{2}+(-\zeta_{110}^{21}-\zeta_{110}^{23}+\cdots)q^{3}+\cdots$

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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.