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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 375 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
795.1.bb.a	$795$	$1$	795.bb	795.ab	$26$	$24$	$2$	$0.397$	$\Q(\zeta_{52})$	$D_{26}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{52}^{9}-\zeta_{52}^{11})q^{2}+\zeta_{52}q^{3}+(\zeta_{52}^{18}+\cdots)q^{4}+\cdots$
975.1.cj.a	$975$	$1$	975.cj	975.bj	$30$	$16$	$2$	$0.487$	$\Q(\zeta_{60})$	$A_{5}$	None	None		$8$	$0$	$0$	$0$	$0$	$-8$	$1$		$q+(-\zeta_{60}^{11}+\zeta_{60}^{17})q^{2}+\zeta_{60}^{23}q^{3}+\cdots$
1012.1.r.a	$1012$	$1$	1012.r	253.k	$22$	$20$	$2$	$0.505$	$\Q(\zeta_{33})$	$D_{33}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$2$	$0$	$1$		$q+(\zeta_{66}^{2}-\zeta_{66}^{19})q^{3}+(-\zeta_{66}^{25}+\zeta_{66}^{32}+\cdots)q^{5}+\cdots$
1044.1.bi.a	$1044$	$1$	1044.bi	348.v	$28$	$24$	$2$	$0.521$	$\Q(\zeta_{56})$	$D_{28}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{56}^{25}q^{2}-\zeta_{56}^{22}q^{4}+(\zeta_{56}^{13}+\cdots)q^{5}+\cdots$
1081.1.l.b	$1081$	$1$	1081.l	1081.l	$46$	$44$	$2$	$0.539$	$\Q(\zeta_{69})$	$D_{69}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$2$	$2$	$0$	$0$	$1$		$q+(-\zeta_{138}^{25}-\zeta_{138}^{41})q^{2}+(-\zeta_{138}^{5}+\cdots)q^{3}+\cdots$
1089.1.s.b	$1089$	$1$	1089.s	99.o	$30$	$16$	$2$	$0.543$	16.0.$\cdots$.1	$S_{4}$	None	None		$16$	$0$	$0$	$-2$	$-2$	$0$	$1$		$q+\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+(\beta _{3}+\beta _{15})q^{5}+\cdots$
1220.1.ck.c	$1220$	$1$	1220.ck	1220.bk	$30$	$16$	$2$	$0.609$	$\Q(\zeta_{60})$	$D_{30}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$2$	$0$	$1$		$q-\zeta_{60}^{7}q^{2}+(\zeta_{60}^{25}-\zeta_{60}^{29})q^{3}+\cdots$
1272.1.bh.a	$1272$	$1$	1272.bh	1272.ah	$26$	$24$	$2$	$0.635$	$\Q(\zeta_{52})$	$D_{26}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$-4$	$1$		$q+\zeta_{52}^{25}q^{2}-\zeta_{52}^{9}q^{3}-\zeta_{52}^{24}q^{4}+\cdots$
1288.1.bi.e	$1288$	$1$	1288.bi	1288.ai	$22$	$20$	$2$	$0.643$	$\Q(\zeta_{44})$	$D_{22}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$2$	$0$	$0$	$2$	$11$		$q+\zeta_{44}^{18}q^{2}+(\zeta_{44}^{11}+\zeta_{44}^{13})q^{3}+\cdots$
1332.1.dm.a	$1332$	$1$	1332.dm	444.ai	$36$	$24$	$2$	$0.665$	$\Q(\zeta_{72})$	$D_{36}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{72}^{35}q^{2}-\zeta_{72}^{34}q^{4}+(-\zeta_{72}^{3}+\cdots)q^{5}+\cdots$
1357.1.j.b	$1357$	$1$	1357.j	1357.j	$58$	$56$	$2$	$0.677$	$\Q(\zeta_{87})$	$D_{87}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$2$	$2$	$0$	$0$	$29$		$q+(-\zeta_{174}^{5}-\zeta_{174}^{61})q^{2}+(\zeta_{174}^{8}-\zeta_{174}^{73}+\cdots)q^{3}+\cdots$
86.2.g.b	$86$	$2$	86.g	43.g	$21$	$24$	$2$	$0.687$		$_{}$	None	None		$2$	$0$	$-4$	$-6$	$3$	$3$		$\mathrm{SU}(2)[C_{21}]$
1380.1.bn.a	$1380$	$1$	1380.bn	1380.an	$22$	$20$	$2$	$0.689$	$\Q(\zeta_{44})$	$D_{22}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+\zeta_{44}^{21}q^{2}+\zeta_{44}^{13}q^{3}-\zeta_{44}^{20}q^{4}+\cdots$
1380.1.bn.b	$1380$	$1$	1380.bn	1380.an	$22$	$20$	$2$	$0.689$	$\Q(\zeta_{44})$	$D_{22}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{44}^{13}q^{2}+\zeta_{44}^{3}q^{3}-\zeta_{44}^{4}q^{4}+\cdots$
1380.1.bn.c	$1380$	$1$	1380.bn	1380.an	$22$	$20$	$2$	$0.689$	$\Q(\zeta_{44})$	$D_{22}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{44}^{7}q^{2}+\zeta_{44}^{3}q^{3}+\zeta_{44}^{14}q^{4}+\cdots$
1380.1.bn.d	$1380$	$1$	1380.bn	1380.an	$22$	$20$	$2$	$0.689$	$\Q(\zeta_{44})$	$D_{22}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$2$	$0$	$1$		$q+\zeta_{44}^{21}q^{2}-\zeta_{44}^{15}q^{3}-\zeta_{44}^{20}q^{4}+\cdots$
1395.1.dw.a	$1395$	$1$	1395.dw	155.v	$30$	$16$	$2$	$0.696$	$\Q(\zeta_{60})$	$D_{30}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{60}^{7}+\zeta_{60}^{11})q^{2}+(\zeta_{60}^{14}+\zeta_{60}^{18}+\cdots)q^{4}+\cdots$
1425.1.cd.a	$1425$	$1$	1425.cd	285.aj	$36$	$24$	$2$	$0.711$	$\Q(\zeta_{72})$	$D_{18}$	$\Q(\sqrt{-15}) $	None		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{72}^{3}+\zeta_{72}^{35})q^{2}+\zeta_{72}^{13}q^{3}+\cdots$
1425.1.cd.b	$1425$	$1$	1425.cd	285.aj	$36$	$24$	$2$	$0.711$	$\Q(\zeta_{72})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{72}^{31}q^{3}+\zeta_{72}^{2}q^{4}+(\zeta_{72}^{5}+\zeta_{72}^{25}+\cdots)q^{7}+\cdots$
1449.1.bq.b	$1449$	$1$	1449.bq	161.l	$22$	$20$	$2$	$0.723$	$\Q(\zeta_{44})$	$D_{22}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$2$	$1$		$q+(-\zeta_{44}^{5}-\zeta_{44}^{7})q^{2}+(\zeta_{44}^{10}+\zeta_{44}^{12}+\cdots)q^{4}+\cdots$
1457.1.s.b	$1457$	$1$	1457.s	1457.s	$46$	$44$	$2$	$0.727$	$\Q(\zeta_{69})$	$D_{69}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$2$	$0$	$2$	$2$	$23$		$q+(\zeta_{138}^{58}-\zeta_{138}^{59})q^{2}+(-\zeta_{138}^{47}+\cdots)q^{4}+\cdots$
94.2.c.a	$94$	$2$	94.c	47.c	$23$	$44$	$2$	$0.751$		$_{}$	None	None		$2$	$0$	$-2$	$-4$	$-6$	$-8$		$\mathrm{SU}(2)[C_{23}]$
94.2.c.b	$94$	$2$	94.c	47.c	$23$	$44$	$2$	$0.751$		$_{}$	None	None		$2$	$0$	$2$	$0$	$-4$	$4$		$\mathrm{SU}(2)[C_{23}]$
1564.1.w.c	$1564$	$1$	1564.w	1564.w	$22$	$20$	$2$	$0.781$	$\Q(\zeta_{44})$	$D_{22}$	$\Q(\sqrt{-17}) $	None		$8$	$0$	$2$	$0$	$0$	$0$	$1$		$q+\zeta_{44}^{10}q^{2}+(-\zeta_{44}^{7}-\zeta_{44}^{21})q^{3}+\cdots$
98.2.g.a	$98$	$2$	98.g	49.g	$21$	$24$	$2$	$0.783$		$_{}$	None	None		$2$	$0$	$-2$	$7$	$0$	$0$		$\mathrm{SU}(2)[C_{21}]$
98.2.g.b	$98$	$2$	98.g	49.g	$21$	$24$	$2$	$0.783$		$_{}$	None	None		$2$	$0$	$2$	$-7$	$0$	$0$		$\mathrm{SU}(2)[C_{21}]$
1587.1.h.b	$1587$	$1$	1587.h	69.h	$22$	$20$	$2$	$0.792$	$\Q(\zeta_{33})$	$D_{6}$	$\Q(\sqrt{-23}) $	None		$40$	$0$	$0$	$1$	$0$	$0$	$1$		$q+(\zeta_{66}^{7}-\zeta_{66}^{29})q^{2}-\zeta_{66}q^{3}+(\zeta_{66}^{3}+\cdots)q^{4}+\cdots$
1587.1.h.c	$1587$	$1$	1587.h	69.h	$22$	$20$	$2$	$0.792$	20.0.$\cdots$.6	$D_{4}$	$\Q(\sqrt{-3}) $	None		$40$	$0$	$0$	$2$	$0$	$0$	$1$		$q-\beta _{8}q^{3}+\beta _{2}q^{4}-\beta _{15}q^{7}+\beta _{16}q^{9}+\cdots$
1628.1.bv.a	$1628$	$1$	1628.bv	1628.av	$30$	$16$	$2$	$0.812$	$\Q(\zeta_{60})$	$A_{5}$	None	None		$8$	$0$	$0$	$0$	$-6$	$0$	$1$		$q+\zeta_{60}^{11}q^{2}+(\zeta_{60}^{7}+\zeta_{60}^{19})q^{3}+\cdots$
1633.1.t.b	$1633$	$1$	1633.t	1633.t	$70$	$48$	$2$	$0.815$	$\Q(\zeta_{210})$	$D_{105}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$-2$	$3$	$0$	$0$	$1$		$q+(\zeta_{210}^{4}+\zeta_{210}^{32})q^{2}+(-\zeta_{210}^{25}+\zeta_{210}^{26}+\cdots)q^{3}+\cdots$
1677.1.cz.c	$1677$	$1$	1677.cz	1677.bz	$42$	$24$	$2$	$0.837$	$\Q(\zeta_{84})$	$D_{42}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+(-\zeta_{84}^{5}-\zeta_{84}^{31})q^{2}+\zeta_{84}^{38}q^{3}+\cdots$
1695.1.bt.a	$1695$	$1$	1695.bt	1695.at	$28$	$24$	$2$	$0.846$	$\Q(\zeta_{56})$	$D_{28}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{56}+\zeta_{56}^{7})q^{2}-\zeta_{56}^{19}q^{3}+(\zeta_{56}^{2}+\cdots)q^{4}+\cdots$
1695.1.cl.a	$1695$	$1$	1695.cl	1695.bl	$56$	$48$	$2$	$0.846$	$\Q(\zeta_{112})$	$D_{56}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{112}^{7}+\zeta_{112}^{33})q^{2}-\zeta_{112}^{39}q^{3}+\cdots$
1705.1.ek.e	$1705$	$1$	1705.ek	1705.dk	$30$	$16$	$2$	$0.851$	$\Q(\zeta_{60})$	$D_{30}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$8$	$0$	$1$		$q+(\zeta_{60}^{11}+\zeta_{60}^{13})q^{2}+(\zeta_{60}^{22}+\zeta_{60}^{24}+\cdots)q^{4}+\cdots$
1725.1.bc.a	$1725$	$1$	1725.bc	69.h	$22$	$20$	$2$	$0.861$	$\Q(\zeta_{44})$	$D_{11}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{44}^{3}+\zeta_{44}^{5})q^{2}-\zeta_{44}^{21}q^{3}+\cdots$
1725.1.bg.a	$1725$	$1$	1725.bg	345.u	$44$	$40$	$2$	$0.861$	$\Q(\zeta_{88})$	$D_{22}$	$\Q(\sqrt{-15}) $	None		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{88}^{9}+\zeta_{88}^{37})q^{2}-\zeta_{88}^{19}q^{3}+\cdots$
1740.1.cf.a	$1740$	$1$	1740.cf	1740.bf	$28$	$24$	$2$	$0.868$	$\Q(\zeta_{56})$	$D_{28}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$-4$	$0$	$1$		$q-\zeta_{56}^{17}q^{2}-\zeta_{56}^{25}q^{3}-\zeta_{56}^{6}q^{4}+\cdots$
1740.1.cf.b	$1740$	$1$	1740.cf	1740.bf	$28$	$24$	$2$	$0.868$	$\Q(\zeta_{56})$	$D_{28}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$4$	$0$	$1$		$q+\zeta_{56}^{17}q^{2}-\zeta_{56}^{5}q^{3}-\zeta_{56}^{6}q^{4}+\cdots$
1748.1.bc.a	$1748$	$1$	1748.bc	437.o	$22$	$20$	$2$	$0.872$	$\Q(\zeta_{33})$	$D_{33}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$2$	$2$	$11$		$q+(-\zeta_{66}^{7}-\zeta_{66}^{17})q^{5}+(-\zeta_{66}^{29}+\cdots)q^{7}+\cdots$
1771.1.bn.a	$1771$	$1$	1771.bn	1771.an	$30$	$16$	$2$	$0.884$	$\Q(\zeta_{60})$	$A_{5}$	None	None		$8$	$0$	$6$	$-2$	$0$	$0$	$1$		$q+(-\zeta_{60}^{4}+\zeta_{60}^{10})q^{2}+\zeta_{60}^{26}q^{3}+\cdots$
1800.1.dg.a	$1800$	$1$	1800.dg	1800.cg	$30$	$16$	$2$	$0.898$	$\Q(\zeta_{60})$	$A_{5}$	None	None		$8$	$0$	$0$	$4$	$0$	$0$	$1$		$q+\zeta_{60}^{29}q^{2}+\zeta_{60}^{18}q^{3}-\zeta_{60}^{28}q^{4}+\cdots$
1827.1.cw.a	$1827$	$1$	1827.cw	609.aj	$28$	$24$	$2$	$0.912$	$\Q(\zeta_{56})$	$D_{28}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$-4$	$1$		$q+(\zeta_{56}^{19}-\zeta_{56}^{27})q^{2}+(-\zeta_{56}^{10}+\cdots)q^{4}+\cdots$
1827.1.cw.b	$1827$	$1$	1827.cw	609.aj	$28$	$24$	$2$	$0.912$	$\Q(\zeta_{56})$	$D_{28}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$4$	$1$		$q+(\zeta_{56}^{19}+\zeta_{56}^{27})q^{2}+(-\zeta_{56}^{10}+\cdots)q^{4}+\cdots$
1829.1.r.b	$1829$	$1$	1829.r	1829.r	$58$	$56$	$2$	$0.913$	$\Q(\zeta_{87})$	$D_{87}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$2$	$0$	$2$	$2$	$1$		$q+(\zeta_{174}^{28}-\zeta_{174}^{71})q^{2}+(\zeta_{174}^{12}-\zeta_{174}^{55}+\cdots)q^{4}+\cdots$
1833.1.z.c	$1833$	$1$	1833.z	1833.z	$46$	$44$	$2$	$0.915$	$\Q(\zeta_{92})$	$D_{46}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$2$	$0$	$0$	$1$		$q+(-\zeta_{92}^{5}-\zeta_{92}^{39})q^{2}-\zeta_{92}^{4}q^{3}+\cdots$
1840.1.bq.a	$1840$	$1$	1840.bq	460.n	$22$	$20$	$2$	$0.918$	$\Q(\zeta_{44})$	$D_{22}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$2$	$0$	$1$		$q+(-\zeta_{44}^{7}-\zeta_{44}^{9})q^{3}+\zeta_{44}^{6}q^{5}+\cdots$
1848.1.ec.a	$1848$	$1$	1848.ec	1848.dc	$30$	$16$	$2$	$0.922$	$\Q(\zeta_{60})$	$D_{30}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$2$	$1$		$q-\zeta_{60}^{13}q^{2}+\zeta_{60}^{29}q^{3}+\zeta_{60}^{26}q^{4}+\cdots$
1848.1.ec.b	$1848$	$1$	1848.ec	1848.dc	$30$	$16$	$2$	$0.922$	$\Q(\zeta_{60})$	$D_{30}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-\zeta_{60}^{13}q^{2}-\zeta_{60}^{29}q^{3}+\zeta_{60}^{26}q^{4}+\cdots$
118.2.c.a	$118$	$2$	118.c	59.c	$29$	$56$	$2$	$0.942$		$_{}$	None	None		$2$	$0$	$2$	$-1$	$1$	$4$		$\mathrm{SU}(2)[C_{29}]$
1908.1.bf.a	$1908$	$1$	1908.bf	212.h	$26$	$24$	$2$	$0.952$	$\Q(\zeta_{52})$	$D_{26}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{52}^{23}q^{2}-\zeta_{52}^{20}q^{4}+(\zeta_{52}^{9}+\zeta_{52}^{21}+\cdots)q^{5}+\cdots$

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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.