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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 888 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
2036.1.j.a	$2036$	$1$	2036.j	2036.j	$254$	$126$	$1$	$1.016$	$\Q(\zeta_{254})$	$D_{127}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{254}^{55}q^{2}+\zeta_{254}^{110}q^{4}+(\zeta_{254}^{48}+\cdots)q^{5}+\cdots$
2181.1.s.a	$2181$	$1$	2181.s	2181.s	$242$	$110$	$1$	$1.088$	$\Q(\zeta_{242})$	$D_{121}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{242}^{39}q^{3}-\zeta_{242}^{105}q^{4}+(\zeta_{242}^{54}+\cdots)q^{7}+\cdots$
2228.1.i.a	$2228$	$1$	2228.i	2228.i	$278$	$138$	$1$	$1.112$	$\Q(\zeta_{278})$	$D_{139}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{278}^{109}q^{2}-\zeta_{278}^{79}q^{4}+(-\zeta_{278}^{9}+\cdots)q^{5}+\cdots$
2361.1.l.a	$2361$	$1$	2361.l	2361.l	$262$	$130$	$1$	$1.178$	$\Q(\zeta_{262})$	$D_{131}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{262}^{123}q^{3}-\zeta_{262}^{83}q^{4}+(-\zeta_{262}^{39}+\cdots)q^{7}+\cdots$
2429.1.j.a	$2429$	$1$	2429.j	2429.j	$346$	$172$	$1$	$1.212$	$\Q(\zeta_{346})$	$D_{173}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$	$1$		$q+(-\zeta_{346}^{35}+\zeta_{346}^{54})q^{2}+(\zeta_{346}^{70}+\cdots)q^{4}+\cdots$
2469.1.l.a	$2469$	$1$	2469.l	2469.l	$274$	$136$	$1$	$1.232$	$\Q(\zeta_{274})$	$D_{137}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q+\zeta_{274}^{136}q^{3}+\zeta_{274}^{94}q^{4}+(-\zeta_{274}^{101}+\cdots)q^{7}+\cdots$
2513.1.l.a	$2513$	$1$	2513.l	2513.l	$358$	$178$	$1$	$1.254$	$\Q(\zeta_{358})$	$D_{179}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$	$1$		$q+(-\zeta_{358}^{35}-\zeta_{358}^{149})q^{2}+(-\zeta_{358}^{5}+\cdots)q^{4}+\cdots$
2577.1.z.a	$2577$	$1$	2577.z	2577.z	$286$	$120$	$1$	$1.286$	$\Q(\zeta_{143})$	$D_{143}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$2$	$1$		$q-\zeta_{286}^{5}q^{3}-\zeta_{286}^{83}q^{4}+(\zeta_{286}^{54}-\zeta_{286}^{87}+\cdots)q^{7}+\cdots$
2612.1.i.a	$2612$	$1$	2612.i	2612.i	$326$	$162$	$1$	$1.304$	$\Q(\zeta_{326})$	$D_{163}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{326}^{53}q^{2}+\zeta_{326}^{106}q^{4}+(\zeta_{326}^{74}+\cdots)q^{5}+\cdots$
2653.1.de.a	$2653$	$1$	2653.de	2653.ce	$378$	$108$	$1$	$1.324$	$\Q(\zeta_{189})$	$D_{189}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{378}^{102}+\zeta_{378}^{176})q^{2}+(-\zeta_{378}^{15}+\cdots)q^{4}+\cdots$
2708.1.p.a	$2708$	$1$	2708.p	2708.p	$338$	$156$	$1$	$1.351$	$\Q(\zeta_{338})$	$D_{169}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{338}^{129}q^{2}-\zeta_{338}^{89}q^{4}+(\zeta_{338}^{8}-\zeta_{338}^{141}+\cdots)q^{5}+\cdots$
2721.1.k.a	$2721$	$1$	2721.k	2721.k	$302$	$150$	$1$	$1.358$	$\Q(\zeta_{302})$	$D_{151}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{302}^{121}q^{3}+\zeta_{302}^{138}q^{4}+(\zeta_{302}^{40}+\cdots)q^{7}+\cdots$
2773.1.j.b	$2773$	$1$	2773.j	2773.j	$58$	$112$	$4$	$1.384$	$\Q(\zeta_{145})$	$D_{145}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$2$	$2$	$0$	$2$	$1$		$q+(\zeta_{290}^{84}+\zeta_{290}^{106})q^{2}+(-\zeta_{290}^{27}+\cdots)q^{3}+\cdots$
2776.1.l.a	$2776$	$1$	2776.l	2776.l	$346$	$172$	$1$	$1.385$	$\Q(\zeta_{346})$	$D_{173}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q+\zeta_{346}^{38}q^{2}+(-\zeta_{346}^{35}-\zeta_{346}^{99}+\cdots)q^{3}+\cdots$
2804.1.bg.a	$2804$	$1$	2804.bg	2804.ag	$350$	$120$	$1$	$1.399$	$\Q(\zeta_{175})$	$D_{175}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{350}^{58}q^{2}+\zeta_{350}^{116}q^{4}+(-\zeta_{350}^{27}+\cdots)q^{5}+\cdots$
2836.1.t.a	$2836$	$1$	2836.t	2836.t	$354$	$116$	$1$	$1.415$	$\Q(\zeta_{177})$	$D_{177}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$-1$	$0$	$1$		$q+\zeta_{354}^{110}q^{2}-\zeta_{354}^{43}q^{4}+(\zeta_{354}^{90}+\cdots)q^{5}+\cdots$
2883.1.z.a	$2883$	$1$	2883.z	2883.z	$310$	$120$	$1$	$1.439$	$\Q(\zeta_{155})$	$D_{155}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$2$	$1$		$q-\zeta_{310}^{107}q^{3}-\zeta_{310}^{81}q^{4}+(-\zeta_{310}^{89}+\cdots)q^{7}+\cdots$
2888.1.bs.a	$2888$	$1$	2888.bs	2888.as	$342$	$108$	$1$	$1.441$	$\Q(\zeta_{171})$	$D_{171}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$3$	$0$	$0$	$1$		$q+\zeta_{342}^{70}q^{2}+(\zeta_{342}^{152}+\zeta_{342}^{156})q^{3}+\cdots$
2901.1.z.a	$2901$	$1$	2901.z	2901.z	$322$	$132$	$1$	$1.448$	$\Q(\zeta_{161})$	$D_{161}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-5$	$1$		$q+\zeta_{322}^{66}q^{3}-\zeta_{322}^{31}q^{4}+(-\zeta_{322}^{21}+\cdots)q^{7}+\cdots$
2921.1.bg.a	$2921$	$1$	2921.bg	2921.ag	$126$	$108$	$3$	$1.458$	$\Q(\zeta_{189})$	$D_{189}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{378}^{158}+\zeta_{378}^{166})q^{2}+(\zeta_{378}^{10}+\zeta_{378}^{68}+\cdots)q^{3}+\cdots$
2932.1.t.a	$2932$	$1$	2932.t	2932.t	$366$	$120$	$1$	$1.463$	$\Q(\zeta_{183})$	$D_{183}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$2$	$0$	$1$		$q-\zeta_{366}^{153}q^{2}-\zeta_{366}^{123}q^{4}+(-\zeta_{366}^{157}+\cdots)q^{5}+\cdots$
3017.1.ba.a	$3017$	$1$	3017.ba	3017.aa	$430$	$168$	$1$	$1.506$	$\Q(\zeta_{215})$	$D_{215}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$1$	$1$		$q+(\zeta_{430}^{26}-\zeta_{430}^{209})q^{2}+(\zeta_{430}^{20}+\zeta_{430}^{52}+\cdots)q^{4}+\cdots$
3028.1.bt.a	$3028$	$1$	3028.bt	3028.at	$378$	$108$	$1$	$1.511$	$\Q(\zeta_{189})$	$D_{189}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{378}^{110}q^{2}-\zeta_{378}^{31}q^{4}+(-\zeta_{378}^{163}+\cdots)q^{5}+\cdots$
3032.1.cg.a	$3032$	$1$	3032.cg	3032.bg	$378$	$108$	$1$	$1.513$	$\Q(\zeta_{189})$	$D_{189}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-18$	$0$	$0$	$1$		$q+\zeta_{378}^{58}q^{2}+(\zeta_{378}^{70}-\zeta_{378}^{135})q^{3}+\cdots$
3092.1.i.a	$3092$	$1$	3092.i	3092.i	$386$	$192$	$1$	$1.543$	$\Q(\zeta_{386})$	$D_{193}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{386}^{151}q^{2}-\zeta_{386}^{109}q^{4}+(\zeta_{386}^{76}+\cdots)q^{5}+\cdots$
3101.1.bb.a	$3101$	$1$	3101.bb	3101.ab	$442$	$192$	$1$	$1.548$	$\Q(\zeta_{221})$	$D_{221}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$1$	$1$		$q+(\zeta_{442}^{38}+\zeta_{442}^{218})q^{2}+(-\zeta_{442}^{35}+\cdots)q^{4}+\cdots$
3117.1.l.a	$3117$	$1$	3117.l	3117.l	$346$	$172$	$1$	$1.556$	$\Q(\zeta_{346})$	$D_{173}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q+\zeta_{346}^{150}q^{3}+\zeta_{346}^{54}q^{4}+(\zeta_{346}^{30}+\cdots)q^{7}+\cdots$
3153.1.br.a	$3153$	$1$	3153.br	3153.ar	$350$	$120$	$1$	$1.574$	$\Q(\zeta_{175})$	$D_{175}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$5$	$0$	$0$	$1$		$q+\zeta_{350}^{160}q^{3}+\zeta_{350}^{166}q^{4}+(-\zeta_{350}^{101}+\cdots)q^{7}+\cdots$
3188.1.i.a	$3188$	$1$	3188.i	3188.i	$398$	$198$	$1$	$1.591$	$\Q(\zeta_{398})$	$D_{199}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{398}^{43}q^{2}+\zeta_{398}^{86}q^{4}+(\zeta_{398}^{40}+\cdots)q^{5}+\cdots$
3189.1.s.a	$3189$	$1$	3189.s	3189.s	$354$	$116$	$1$	$1.592$	$\Q(\zeta_{177})$	$D_{177}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$2$	$1$		$q-\zeta_{354}^{85}q^{3}+\zeta_{354}^{98}q^{4}+(\zeta_{354}^{100}+\cdots)q^{7}+\cdots$
3197.1.x.a	$3197$	$1$	3197.x	3197.x	$138$	$132$	$3$	$1.596$	$\Q(\zeta_{207})$	$D_{207}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{414}^{44}-\zeta_{414}^{151})q^{2}+(\zeta_{414}^{8}-\zeta_{414}^{121}+\cdots)q^{3}+\cdots$
3241.1.cu.a	$3241$	$1$	3241.cu	3241.bu	$462$	$120$	$1$	$1.617$	$\Q(\zeta_{462})$	$D_{231}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$1$	$0$	$0$	$2$	$1$		$q+(\zeta_{462}^{54}-\zeta_{462}^{115})q^{2}+(\zeta_{462}^{108}-\zeta_{462}^{169}+\cdots)q^{4}+\cdots$
3261.1.l.a	$3261$	$1$	3261.l	3261.l	$362$	$180$	$1$	$1.627$	$\Q(\zeta_{362})$	$D_{181}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{362}^{99}q^{3}-\zeta_{362}^{35}q^{4}+(\zeta_{362}^{148}+\cdots)q^{7}+\cdots$
3284.1.t.a	$3284$	$1$	3284.t	3284.t	$410$	$160$	$1$	$1.639$	$\Q(\zeta_{205})$	$D_{205}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$-3$	$0$	$1$		$q-\zeta_{410}^{23}q^{2}+\zeta_{410}^{46}q^{4}+(\zeta_{410}^{30}+\cdots)q^{5}+\cdots$
3316.1.bg.a	$3316$	$1$	3316.bg	3316.ag	$414$	$132$	$1$	$1.655$	$\Q(\zeta_{207})$	$D_{207}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$3$	$0$	$1$		$q-\zeta_{414}^{47}q^{2}+\zeta_{414}^{94}q^{4}+(-\zeta_{414}^{59}+\cdots)q^{5}+\cdots$
3317.1.r.b	$3317$	$1$	3317.r	3317.r	$106$	$104$	$2$	$1.655$	$\Q(\zeta_{159})$	$D_{159}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$2$	$0$	$2$	$2$	$1$		$q+(-\zeta_{318}^{83}-\zeta_{318}^{133})q^{2}+(-\zeta_{318}^{7}+\cdots)q^{4}+\cdots$
3337.1.t.a	$3337$	$1$	3337.t	3337.t	$70$	$120$	$5$	$1.665$	$\Q(\zeta_{175})$	$D_{175}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{350}^{58}+\zeta_{350}^{172})q^{2}+(\zeta_{350}^{76}+\zeta_{350}^{104}+\cdots)q^{3}+\cdots$
3352.1.be.a	$3352$	$1$	3352.be	3352.ae	$418$	$180$	$1$	$1.673$	$\Q(\zeta_{209})$	$D_{209}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$2$	$0$	$0$	$1$		$q-\zeta_{418}^{25}q^{2}+(\zeta_{418}^{36}-\zeta_{418}^{157})q^{3}+\cdots$
3364.1.t.a	$3364$	$1$	3364.t	3364.t	$406$	$168$	$1$	$1.679$	$\Q(\zeta_{203})$	$D_{203}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$2$	$0$	$1$		$q-\zeta_{406}^{47}q^{2}+\zeta_{406}^{94}q^{4}+(-\zeta_{406}^{41}+\cdots)q^{5}+\cdots$
3369.1.z.a	$3369$	$1$	3369.z	3369.z	$374$	$160$	$1$	$1.681$	$\Q(\zeta_{187})$	$D_{187}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-9$	$1$		$q-\zeta_{374}^{155}q^{3}-\zeta_{374}^{31}q^{4}+(-\zeta_{374}^{121}+\cdots)q^{7}+\cdots$
3405.1.p.a	$3405$	$1$	3405.p	3405.p	$226$	$112$	$1$	$1.699$	$\Q(\zeta_{226})$	$D_{113}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-2$	$-1$	$-1$	$0$	$1$		$q+(\zeta_{226}^{38}-\zeta_{226}^{79})q^{2}+\zeta_{226}^{92}q^{3}+\cdots$
3405.1.p.b	$3405$	$1$	3405.p	3405.p	$226$	$112$	$1$	$1.699$	$\Q(\zeta_{226})$	$D_{113}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$2$	$1$	$1$	$0$	$1$		$q+(-\zeta_{226}^{38}+\zeta_{226}^{79})q^{2}-\zeta_{226}^{92}q^{3}+\cdots$
3409.1.cj.a	$3409$	$1$	3409.cj	3409.bj	$486$	$162$	$1$	$1.701$	$\Q(\zeta_{486})$	$D_{243}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{486}^{46}+\zeta_{486}^{118})q^{2}+(\zeta_{486}^{92}+\zeta_{486}^{164}+\cdots)q^{4}+\cdots$
3412.1.u.a	$3412$	$1$	3412.u	3412.u	$426$	$140$	$1$	$1.703$	$\Q(\zeta_{213})$	$D_{213}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$2$	$0$	$1$		$q-\zeta_{426}^{89}q^{2}+\zeta_{426}^{178}q^{4}+(\zeta_{426}^{112}+\cdots)q^{5}+\cdots$
3421.1.bv.a	$3421$	$1$	3421.bv	3421.av	$310$	$120$	$1$	$1.707$	$\Q(\zeta_{155})$	$D_{155}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$-3$	$0$	$1$		$q+(\zeta_{310}^{98}+\zeta_{310}^{108})q^{3}-\zeta_{310}^{73}q^{4}+\cdots$
3428.1.j.a	$3428$	$1$	3428.j	3428.j	$214$	$106$	$1$	$1.711$	$\Q(\zeta_{214})$	$D_{214}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-\zeta_{214}^{19}q^{2}+\zeta_{214}^{38}q^{4}+(\zeta_{214}^{6}+\zeta_{214}^{95}+\cdots)q^{5}+\cdots$
3428.1.k.a	$3428$	$1$	3428.k	3428.k	$214$	$106$	$1$	$1.711$	$\Q(\zeta_{214})$	$D_{107}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{214}^{59}q^{2}-\zeta_{214}^{11}q^{4}+(-\zeta_{214}^{13}+\cdots)q^{5}+\cdots$
3437.1.bp.a	$3437$	$1$	3437.bp	3437.ap	$490$	$168$	$1$	$1.715$	$\Q(\zeta_{245})$	$D_{245}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$7$	$0$	$0$	$0$	$1$		$q+(-\zeta_{490}^{63}-\zeta_{490}^{103})q^{2}+(\zeta_{490}^{126}+\cdots)q^{4}+\cdots$
3493.1.bc.a	$3493$	$1$	3493.bc	3493.ac	$498$	$164$	$1$	$1.743$	$\Q(\zeta_{249})$	$D_{249}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$1$	$1$		$q+(\zeta_{498}^{190}-\zeta_{498}^{215})q^{2}+(-\zeta_{498}^{131}+\cdots)q^{4}+\cdots$
3495.1.bk.a	$3495$	$1$	3495.bk	3495.ak	$116$	$112$	$2$	$1.744$	$\Q(\zeta_{232})$	$D_{116}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{232}^{11}-\zeta_{232}^{45})q^{2}+\zeta_{232}^{89}q^{3}+\cdots$

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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.