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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 122 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
356.1.j.a	$356$	$1$	356.j	356.j	$22$	$10$	$1$	$0.178$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$-2$	$0$	$1$		$q+\zeta_{22}^{3}q^{2}+\zeta_{22}^{6}q^{4}+(\zeta_{22}^{8}+\zeta_{22}^{10}+\cdots)q^{5}+\cdots$
603.1.x.a	$603$	$1$	603.x	67.f	$22$	$10$	$1$	$0.301$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{22}^{5}q^{4}+(\zeta_{22}^{2}+\zeta_{22}^{3})q^{7}+(-\zeta_{22}+\cdots)q^{13}+\cdots$
644.1.r.a	$644$	$1$	644.r	644.r	$22$	$10$	$1$	$0.321$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q+\zeta_{22}^{6}q^{2}-\zeta_{22}q^{4}-\zeta_{22}^{9}q^{7}-\zeta_{22}^{7}q^{8}+\cdots$
644.1.r.b	$644$	$1$	644.r	644.r	$22$	$10$	$1$	$0.321$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-1$	$0$	$0$	$1$	$1$		$q+\zeta_{22}^{4}q^{2}+\zeta_{22}^{8}q^{4}+\zeta_{22}^{9}q^{7}+\cdots$
712.1.w.a	$712$	$1$	712.w	712.w	$22$	$10$	$1$	$0.355$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-\zeta_{22}^{9}q^{2}+(\zeta_{22}^{3}-\zeta_{22}^{5})q^{3}-\zeta_{22}^{7}q^{4}+\cdots$
759.1.r.a	$759$	$1$	759.r	759.r	$22$	$10$	$1$	$0.379$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$1$	$-2$	$0$	$1$		$q-\zeta_{22}^{4}q^{3}-\zeta_{22}^{2}q^{4}+(-\zeta_{22}^{5}-\zeta_{22}^{7}+\cdots)q^{5}+\cdots$
759.1.r.b	$759$	$1$	759.r	759.r	$22$	$10$	$1$	$0.379$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$1$	$2$	$0$	$1$		$q+\zeta_{22}q^{3}-\zeta_{22}^{2}q^{4}+(\zeta_{22}^{5}+\zeta_{22}^{7}+\cdots)q^{5}+\cdots$
979.1.r.a	$979$	$1$	979.r	979.r	$22$	$10$	$1$	$0.489$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-11$	$2$	$0$	$1$		$q+(-1-\zeta_{22}^{5})q^{3}-\zeta_{22}^{3}q^{4}+(-\zeta_{22}^{2}+\cdots)q^{5}+\cdots$
1035.1.bd.a	$1035$	$1$	1035.bd	115.i	$22$	$10$	$1$	$0.517$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+(\zeta_{22}^{2}-\zeta_{22}^{10})q^{2}+(\zeta_{22}+\zeta_{22}^{4}+\cdots)q^{4}+\cdots$
1035.1.bd.b	$1035$	$1$	1035.bd	115.i	$22$	$10$	$1$	$0.517$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+(-\zeta_{22}^{2}+\zeta_{22}^{10})q^{2}+(\zeta_{22}+\zeta_{22}^{4}+\cdots)q^{4}+\cdots$
1127.1.o.a	$1127$	$1$	1127.o	23.d	$22$	$10$	$1$	$0.562$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+(-\zeta_{22}^{6}+\zeta_{22}^{9})q^{2}+(-\zeta_{22}+\zeta_{22}^{4}+\cdots)q^{4}+\cdots$
1127.1.x.a	$1127$	$1$	1127.x	161.p	$66$	$20$	$1$	$0.562$	$\Q(\zeta_{33})$	$D_{22}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$-2$	$0$	$0$	$0$	$1$		$q+(\zeta_{66}^{5}+\zeta_{66}^{29})q^{2}+(-\zeta_{66}+\zeta_{66}^{10}+\cdots)q^{4}+\cdots$
1139.1.s.a	$1139$	$1$	1139.s	1139.s	$22$	$10$	$1$	$0.568$	$\Q(\zeta_{22})$	$D_{22}$	None	$\Q(\sqrt{17}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{22}^{6}+\zeta_{22}^{8})q^{2}+(-\zeta_{22}+\zeta_{22}^{3}+\cdots)q^{4}+\cdots$
1191.1.r.a	$1191$	$1$	1191.r	1191.r	$22$	$10$	$1$	$0.594$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q+\zeta_{22}^{10}q^{3}+\zeta_{22}^{7}q^{4}-\zeta_{22}^{9}q^{9}+\cdots$
1265.1.ba.a	$1265$	$1$	1265.ba	1265.aa	$22$	$10$	$1$	$0.631$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+(-\zeta_{22}^{2}+\zeta_{22}^{8})q^{3}-\zeta_{22}^{4}q^{4}+\cdots$
1265.1.ba.b	$1265$	$1$	1265.ba	1265.aa	$22$	$10$	$1$	$0.631$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+(\zeta_{22}^{2}-\zeta_{22}^{8})q^{3}-\zeta_{22}^{4}q^{4}-\zeta_{22}^{10}q^{5}+\cdots$
1288.1.bi.c	$1288$	$1$	1288.bi	1288.ai	$22$	$10$	$1$	$0.643$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$1$	$0$	$0$	$1$	$1$		$q+\zeta_{22}^{9}q^{2}-\zeta_{22}^{7}q^{4}+\zeta_{22}q^{7}+\zeta_{22}^{5}q^{8}+\cdots$
1288.1.bi.d	$1288$	$1$	1288.bi	1288.ai	$22$	$10$	$1$	$0.643$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$1$	$0$	$0$	$1$	$1$		$q-\zeta_{22}^{8}q^{2}-\zeta_{22}^{5}q^{4}+\zeta_{22}q^{7}-\zeta_{22}^{2}q^{8}+\cdots$
1288.1.bi.e	$1288$	$1$	1288.bi	1288.ai	$22$	$20$	$2$	$0.643$	$\Q(\zeta_{44})$	$D_{22}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$2$	$0$	$0$	$2$	$11$		$q+\zeta_{44}^{18}q^{2}+(\zeta_{44}^{11}+\zeta_{44}^{13})q^{3}+\cdots$
1288.1.bu.a	$1288$	$1$	1288.bu	1288.au	$22$	$10$	$1$	$0.643$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$1$	$0$	$0$	$-1$	$1$		$q+\zeta_{22}^{5}q^{2}+\zeta_{22}^{10}q^{4}-\zeta_{22}^{3}q^{7}+\cdots$
1288.1.bu.b	$1288$	$1$	1288.bu	1288.au	$22$	$10$	$1$	$0.643$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$1$	$0$	$0$	$1$	$1$		$q-\zeta_{22}^{2}q^{2}+\zeta_{22}^{4}q^{4}+\zeta_{22}^{3}q^{7}+\cdots$
1336.1.e.e	$1336$	$1$	1336.e	1336.e	$2$	$10$	$10$	$0.667$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-167}) $	None		$4$	$0$	$1$	$0$	$0$	$-2$	$1$		$q-\zeta_{22}^{6}q^{2}+(\zeta_{22}^{2}+\zeta_{22}^{9})q^{3}-\zeta_{22}q^{4}+\cdots$
1355.1.c.e	$1355$	$1$	1355.c	1355.c	$2$	$10$	$10$	$0.676$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-271}) $	None		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+(-\zeta_{22}-\zeta_{22}^{10})q^{2}+(-1+\zeta_{22}^{2}+\cdots)q^{4}+\cdots$
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		$8$	$0$	$0$	$0$	$2$	$0$	$1$		$q+\zeta_{44}^{21}q^{2}-\zeta_{44}^{15}q^{3}-\zeta_{44}^{20}q^{4}+\cdots$
1391.1.d.e	$1391$	$1$	1391.d	1391.d	$2$	$10$	$10$	$0.694$	$\Q(\zeta_{44})^+$	$D_{22}$	$\Q(\sqrt{-1391}) $	None	✓	$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+(-1+\beta _{2}-\beta _{4}+\beta _{6}+\beta _{8}+\cdots)q^{3}+\cdots$
1407.1.bq.a	$1407$	$1$	1407.bq	1407.aq	$22$	$10$	$1$	$0.702$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$1$	$1$		$q-\zeta_{22}q^{3}-\zeta_{22}^{4}q^{4}-\zeta_{22}^{6}q^{7}+\zeta_{22}^{2}q^{9}+\cdots$
1407.1.bq.b	$1407$	$1$	1407.bq	1407.aq	$22$	$10$	$1$	$0.702$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-1$	$1$		$q+\zeta_{22}q^{3}-\zeta_{22}^{4}q^{4}-\zeta_{22}^{9}q^{7}+\zeta_{22}^{2}q^{9}+\cdots$
1412.1.l.a	$1412$	$1$	1412.l	1412.l	$22$	$10$	$1$	$0.705$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-\zeta_{22}^{3}q^{2}+\zeta_{22}^{6}q^{4}+(\zeta_{22}+\zeta_{22}^{4}+\cdots)q^{5}+\cdots$
1449.1.bq.b	$1449$	$1$	1449.bq	161.l	$22$	$20$	$2$	$0.723$	$\Q(\zeta_{44})$	$D_{22}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$2$	$1$		$q+(-\zeta_{44}^{5}-\zeta_{44}^{7})q^{2}+(\zeta_{44}^{10}+\zeta_{44}^{12}+\cdots)q^{4}+\cdots$
1564.1.w.c	$1564$	$1$	1564.w	1564.w	$22$	$20$	$2$	$0.781$	$\Q(\zeta_{44})$	$D_{22}$	$\Q(\sqrt{-17}) $	None		$8$	$0$	$2$	$0$	$0$	$0$	$1$		$q+\zeta_{44}^{10}q^{2}+(-\zeta_{44}^{7}-\zeta_{44}^{21})q^{3}+\cdots$
1592.1.ba.a	$1592$	$1$	1592.ba	1592.aa	$22$	$10$	$1$	$0.795$	$\Q(\zeta_{22})$	$D_{22}$	None	$\Q(\sqrt{2}) $		$4$	$0$	$1$	$0$	$0$	$-2$	$1$		$q-\zeta_{22}^{6}q^{2}-\zeta_{22}q^{4}+(-\zeta_{22}^{5}-\zeta_{22}^{9}+\cdots)q^{7}+\cdots$
1608.1.bo.a	$1608$	$1$	1608.bo	1608.ao	$22$	$10$	$1$	$0.802$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-\zeta_{22}^{3}q^{2}-\zeta_{22}^{5}q^{3}+\zeta_{22}^{6}q^{4}+\cdots$
1608.1.bo.b	$1608$	$1$	1608.bo	1608.ao	$22$	$10$	$1$	$0.802$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$1$	$0$	$0$	$1$		$q+\zeta_{22}^{3}q^{2}+\zeta_{22}^{9}q^{3}+\zeta_{22}^{6}q^{4}+\cdots$
1631.1.d.d	$1631$	$1$	1631.d	1631.d	$2$	$10$	$10$	$0.814$	$\Q(\zeta_{44})^+$	$D_{22}$	$\Q(\sqrt{-1631}) $	None	✓	$4$	$0$	$-2$	$0$	$0$	$-10$	$1$		$q-\beta _{6}q^{2}-\beta _{1}q^{3}+(1-\beta _{8})q^{4}-\beta _{9}q^{5}+\cdots$
1655.1.d.e	$1655$	$1$	1655.d	1655.d	$2$	$10$	$10$	$0.826$	$\Q(\zeta_{44})^+$	$D_{22}$	$\Q(\sqrt{-1655}) $	None	✓	$4$	$0$	$0$	$0$	$-10$	$0$	$1$		$q-\beta _{1}q^{2}-\beta _{9}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
1725.1.bg.a	$1725$	$1$	1725.bg	345.u	$44$	$40$	$2$	$0.861$	$\Q(\zeta_{88})$	$D_{22}$	$\Q(\sqrt{-15}) $	None		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{88}^{9}+\zeta_{88}^{37})q^{2}-\zeta_{88}^{19}q^{3}+\cdots$
1771.1.bf.a	$1771$	$1$	1771.bf	1771.af	$22$	$10$	$1$	$0.884$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$-1$	$1$		$q+(-\zeta_{22}^{2}-\zeta_{22}^{5})q^{2}+(\zeta_{22}^{4}+\zeta_{22}^{7}+\cdots)q^{4}+\cdots$
1771.1.bf.b	$1771$	$1$	1771.bf	1771.af	$22$	$10$	$1$	$0.884$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$1$	$1$		$q+(\zeta_{22}^{2}+\zeta_{22}^{5})q^{2}+(\zeta_{22}^{4}+\zeta_{22}^{7}+\cdots)q^{4}+\cdots$
1780.1.bj.a	$1780$	$1$	1780.bj	1780.aj	$22$	$10$	$1$	$0.888$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-1$	$0$	$1$	$0$	$1$		$q-\zeta_{22}^{3}q^{2}+(\zeta_{22}^{3}-\zeta_{22}^{7})q^{3}+\zeta_{22}^{6}q^{4}+\cdots$
1780.1.bj.b	$1780$	$1$	1780.bj	1780.aj	$22$	$10$	$1$	$0.888$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$1$	$0$	$1$	$0$	$1$		$q+\zeta_{22}^{3}q^{2}+(-\zeta_{22}^{3}+\zeta_{22}^{7})q^{3}+\cdots$
1791.1.bh.a	$1791$	$1$	1791.bh	199.h	$22$	$10$	$1$	$0.894$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+\zeta_{22}^{3}q^{4}+(\zeta_{22}-\zeta_{22}^{8})q^{7}+(\zeta_{22}^{6}+\cdots)q^{13}+\cdots$
1840.1.bq.a	$1840$	$1$	1840.bq	460.n	$22$	$20$	$2$	$0.918$	$\Q(\zeta_{44})$	$D_{22}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$2$	$0$	$1$		$q+(-\zeta_{44}^{7}-\zeta_{44}^{9})q^{3}+\zeta_{44}^{6}q^{5}+\cdots$
1876.1.bs.a	$1876$	$1$	1876.bs	1876.as	$22$	$10$	$1$	$0.936$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q-\zeta_{22}q^{2}+\zeta_{22}^{2}q^{4}-\zeta_{22}^{9}q^{7}-\zeta_{22}^{3}q^{8}+\cdots$
1876.1.bs.b	$1876$	$1$	1876.bs	1876.as	$22$	$10$	$1$	$0.936$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$1$	$0$	$0$	$1$	$1$		$q-\zeta_{22}^{6}q^{2}-\zeta_{22}q^{4}+\zeta_{22}^{9}q^{7}+\zeta_{22}^{7}q^{8}+\cdots$
1919.1.d.d	$1919$	$1$	1919.d	1919.d	$2$	$10$	$10$	$0.958$	$\Q(\zeta_{44})^+$	$D_{22}$	$\Q(\sqrt{-1919}) $	None	✓	$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q-\beta _{1}q^{2}-\beta _{9}q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots$
1983.1.u.a	$1983$	$1$	1983.u	1983.u	$22$	$10$	$1$	$0.990$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-\zeta_{22}^{7}q^{3}-\zeta_{22}^{4}q^{4}+(-\zeta_{22}^{3}+\zeta_{22}^{9}+\cdots)q^{7}+\cdots$
2004.1.g.e	$2004$	$1$	2004.g	2004.g	$2$	$10$	$10$	$1.000$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-167}) $	None		$4$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q+\zeta_{22}^{6}q^{2}+\zeta_{22}^{2}q^{3}-\zeta_{22}q^{4}+\zeta_{22}^{8}q^{6}+\cdots$

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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.