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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 169 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
336.1.o.a	$336$	$1$	336.o	84.h	$2$	$1$	$1$	$0.168$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{7}) $	✓	$4$	$0$	$0$	$-1$	$0$	$1$	$1$		$q-q^{3}+q^{7}+q^{9}+2q^{19}-q^{21}-q^{25}+\cdots$
336.1.o.b	$336$	$1$	336.o	84.h	$2$	$1$	$1$	$0.168$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{7}) $	✓	$4$	$0$	$0$	$1$	$0$	$-1$	$1$		$q+q^{3}-q^{7}+q^{9}-2q^{19}-q^{21}-q^{25}+\cdots$
420.1.o.a	$420$	$1$	420.o	420.o	$2$	$2$	$2$	$0.210$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{105}) $		$8$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-iq^{2}-iq^{3}-q^{4}-q^{5}-q^{6}-iq^{7}+\cdots$
420.1.o.b	$420$	$1$	420.o	420.o	$2$	$2$	$2$	$0.210$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{105}) $		$8$	$0$	$0$	$0$	$2$	$0$	$1$		$q+iq^{2}-iq^{3}-q^{4}+q^{5}+q^{6}-iq^{7}+\cdots$
756.1.h.a	$756$	$1$	756.h	84.h	$2$	$1$	$1$	$0.377$	$\Q$	$D_{3}$	$\Q(\sqrt{-21}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-1$	$1$		$q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots$
756.1.h.b	$756$	$1$	756.h	84.h	$2$	$1$	$1$	$0.377$	$\Q$	$D_{3}$	$\Q(\sqrt{-21}) $	None	✓	$2$	$0$	$-1$	$0$	$1$	$1$	$1$		$q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots$
756.1.h.c	$756$	$1$	756.h	84.h	$2$	$1$	$1$	$0.377$	$\Q$	$D_{3}$	$\Q(\sqrt{-21}) $	None	✓	$2$	$0$	$1$	$0$	$-1$	$1$	$1$		$q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots$
756.1.h.d	$756$	$1$	756.h	84.h	$2$	$1$	$1$	$0.377$	$\Q$	$D_{3}$	$\Q(\sqrt{-21}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$-1$	$1$		$q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots$
924.1.bk.a	$924$	$1$	924.bk	924.ak	$10$	$4$	$1$	$0.461$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$-1$	$-1$	$3$	$-1$	$1$		$q-\zeta_{10}q^{2}-\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{4}+(1+\cdots)q^{5}+\cdots$
924.1.bk.b	$924$	$1$	924.bk	924.ak	$10$	$4$	$1$	$0.461$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$-1$	$1$	$-3$	$1$	$1$		$q-\zeta_{10}q^{2}+\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots$
924.1.bk.c	$924$	$1$	924.bk	924.ak	$10$	$4$	$1$	$0.461$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$1$	$-1$	$-3$	$-1$	$1$		$q+\zeta_{10}q^{2}-\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots$
924.1.bk.d	$924$	$1$	924.bk	924.ak	$10$	$4$	$1$	$0.461$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$1$	$1$	$3$	$1$	$1$		$q+\zeta_{10}q^{2}+\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{4}+(1+\cdots)q^{5}+\cdots$
1260.1.u.a	$1260$	$1$	1260.u	140.j	$4$	$4$	$2$	$0.629$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-21}) $	None		$8$	$0$	$0$	$0$	$-4$	$0$	$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-q^{5}+\zeta_{8}q^{7}+\cdots$
1260.1.u.b	$1260$	$1$	1260.u	140.j	$4$	$4$	$2$	$0.629$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-21}) $	None		$8$	$0$	$0$	$0$	$4$	$0$	$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+q^{5}-\zeta_{8}q^{7}+\cdots$
1344.1.o.a	$1344$	$1$	1344.o	84.h	$2$	$1$	$1$	$0.671$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{7}) $	✓	$4$	$0$	$0$	$-1$	$0$	$-1$	$1$		$q-q^{3}-q^{7}+q^{9}+2q^{19}+q^{21}-q^{25}+\cdots$
1344.1.o.b	$1344$	$1$	1344.o	84.h	$2$	$1$	$1$	$0.671$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{7}) $	✓	$4$	$0$	$0$	$1$	$0$	$1$	$1$		$q+q^{3}+q^{7}+q^{9}-2q^{19}+q^{21}-q^{25}+\cdots$
1428.1.b.a	$1428$	$1$	1428.b	1428.b	$2$	$2$	$2$	$0.713$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-21}) $, $\Q(\sqrt{-119}) $	$\Q(\sqrt{51}) $		$8$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-q^{2}-iq^{3}+q^{4}+iq^{5}+iq^{6}+iq^{7}+\cdots$
1428.1.b.b	$1428$	$1$	1428.b	1428.b	$2$	$2$	$2$	$0.713$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-21}) $, $\Q(\sqrt{-119}) $	$\Q(\sqrt{51}) $		$8$	$0$	$2$	$0$	$0$	$0$	$1$		$q+q^{2}-iq^{3}+q^{4}-iq^{5}-iq^{6}+iq^{7}+\cdots$
1428.1.r.a	$1428$	$1$	1428.r	1428.r	$4$	$4$	$2$	$0.713$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-21}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}-\zeta_{8}^{3}q^{6}+\cdots$
1428.1.r.b	$1428$	$1$	1428.r	1428.r	$4$	$4$	$2$	$0.713$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-21}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+\zeta_{8}^{3}q^{6}+\cdots$
1428.1.bu.a	$1428$	$1$	1428.bu	1428.au	$8$	$8$	$2$	$0.713$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-21}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{16}^{6}q^{2}-\zeta_{16}q^{3}-\zeta_{16}^{4}q^{4}+(\zeta_{16}^{3}+\cdots)q^{5}+\cdots$
1428.1.bu.b	$1428$	$1$	1428.bu	1428.au	$8$	$8$	$2$	$0.713$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-21}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}^{6}q^{2}-\zeta_{16}q^{3}-\zeta_{16}^{4}q^{4}+(-\zeta_{16}^{3}+\cdots)q^{5}+\cdots$
1596.1.bw.a	$1596$	$1$	1596.bw	1596.aw	$6$	$2$	$1$	$0.797$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$-1$	$-1$	$1$	$2$	$1$		$q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots$
1596.1.bw.b	$1596$	$1$	1596.bw	1596.aw	$6$	$2$	$1$	$0.797$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$-1$	$1$	$-1$	$-2$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\cdots$
1596.1.bw.c	$1596$	$1$	1596.bw	1596.aw	$6$	$2$	$1$	$0.797$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$1$	$-1$	$-1$	$2$	$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\cdots$
1596.1.bw.d	$1596$	$1$	1596.bw	1596.aw	$6$	$2$	$1$	$0.797$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$1$	$1$	$1$	$-2$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots$
1596.1.dt.a	$1596$	$1$	1596.dt	1596.ct	$18$	$6$	$1$	$0.797$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$0$	$0$	$-3$	$-3$	$1$		$q-\zeta_{18}^{7}q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+(-\zeta_{18}^{3}+\cdots)q^{5}+\cdots$
1596.1.dt.b	$1596$	$1$	1596.dt	1596.ct	$18$	$6$	$1$	$0.797$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$0$	$0$	$-3$	$3$	$1$		$q+\zeta_{18}^{7}q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+(-\zeta_{18}^{3}+\cdots)q^{5}+\cdots$
1596.1.dt.c	$1596$	$1$	1596.dt	1596.ct	$18$	$6$	$1$	$0.797$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$0$	$0$	$3$	$-3$	$1$		$q+\zeta_{18}^{7}q^{2}-\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+(\zeta_{18}^{3}+\cdots)q^{5}+\cdots$
1596.1.dt.d	$1596$	$1$	1596.dt	1596.ct	$18$	$6$	$1$	$0.797$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$0$	$0$	$3$	$3$	$1$		$q-\zeta_{18}^{7}q^{2}+\zeta_{18}q^{3}-\zeta_{18}^{5}q^{4}+(\zeta_{18}^{3}+\cdots)q^{5}+\cdots$
1680.1.bb.e	$1680$	$1$	1680.bb	420.o	$2$	$2$	$2$	$0.838$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-35}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{15}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{3}-iq^{5}-iq^{7}-q^{9}-q^{11}+\cdots$
1680.1.bb.f	$1680$	$1$	1680.bb	420.o	$2$	$2$	$2$	$0.838$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-35}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{15}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}-iq^{5}+iq^{7}-q^{9}+q^{11}+\cdots$
1764.1.g.c	$1764$	$1$	1764.g	4.b	$2$	$2$	$2$	$0.880$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{3}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-q^{4}+iq^{8}+iq^{11}+q^{16}+\cdots$
1764.1.y.c	$1764$	$1$	1764.y	28.g	$6$	$4$	$2$	$0.880$	$\Q(\zeta_{12})$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{3}) $		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{8}+\zeta_{12}^{5}q^{11}+\cdots$
1932.1.bi.a	$1932$	$1$	1932.bi	1932.ai	$22$	$10$	$1$	$0.964$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$-1$	$-1$	$-2$	$-1$	$1$		$q-\zeta_{22}^{7}q^{2}-\zeta_{22}q^{3}-\zeta_{22}^{3}q^{4}+(-\zeta_{22}+\cdots)q^{5}+\cdots$
1932.1.bi.b	$1932$	$1$	1932.bi	1932.ai	$22$	$10$	$1$	$0.964$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$-1$	$1$	$2$	$1$	$1$		$q-\zeta_{22}^{7}q^{2}+\zeta_{22}q^{3}-\zeta_{22}^{3}q^{4}+(\zeta_{22}+\cdots)q^{5}+\cdots$
1932.1.bi.c	$1932$	$1$	1932.bi	1932.ai	$22$	$10$	$1$	$0.964$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$1$	$-1$	$2$	$-1$	$1$		$q+\zeta_{22}^{7}q^{2}-\zeta_{22}q^{3}-\zeta_{22}^{3}q^{4}+(\zeta_{22}+\cdots)q^{5}+\cdots$
1932.1.bi.d	$1932$	$1$	1932.bi	1932.ai	$22$	$10$	$1$	$0.964$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$1$	$1$	$-2$	$1$	$1$		$q+\zeta_{22}^{7}q^{2}+\zeta_{22}q^{3}-\zeta_{22}^{3}q^{4}+(-\zeta_{22}+\cdots)q^{5}+\cdots$
2016.1.f.a	$2016$	$1$	2016.f	7.b	$2$	$4$	$4$	$1.006$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-21}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{7}+(-\zeta_{8}+\cdots)q^{11}+\cdots$
2100.1.m.a	$2100$	$1$	2100.m	84.h	$2$	$1$	$1$	$1.048$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{105}) $	✓	$4$	$0$	$-1$	$-1$	$0$	$1$	$1$		$q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots$
2100.1.m.b	$2100$	$1$	2100.m	84.h	$2$	$1$	$1$	$1.048$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{105}) $	✓	$4$	$0$	$-1$	$1$	$0$	$-1$	$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$
2100.1.m.c	$2100$	$1$	2100.m	84.h	$2$	$1$	$1$	$1.048$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{105}) $	✓	$4$	$0$	$1$	$-1$	$0$	$1$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots$
2100.1.m.d	$2100$	$1$	2100.m	84.h	$2$	$1$	$1$	$1.048$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{105}) $	✓	$4$	$0$	$1$	$1$	$0$	$-1$	$1$		$q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots$
2100.1.bq.a	$2100$	$1$	2100.bq	2100.aq	$10$	$8$	$2$	$1.048$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-21}) $	None		$8$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+\zeta_{20}^{7}q^{2}+\zeta_{20}^{9}q^{3}-\zeta_{20}^{4}q^{4}+\cdots$
2100.1.bq.b	$2100$	$1$	2100.bq	2100.aq	$10$	$8$	$2$	$1.048$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-21}) $	None		$8$	$0$	$0$	$0$	$2$	$0$	$1$		$q+\zeta_{20}^{7}q^{2}-\zeta_{20}^{9}q^{3}-\zeta_{20}^{4}q^{4}+\cdots$
2100.1.bs.a	$2100$	$1$	2100.bs	2100.as	$10$	$4$	$1$	$1.048$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$-1$	$-1$	$-1$	$4$	$1$		$q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{3}-\zeta_{10}q^{4}-\zeta_{10}q^{5}+\cdots$
2100.1.bs.b	$2100$	$1$	2100.bs	2100.as	$10$	$4$	$1$	$1.048$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$-1$	$1$	$1$	$-4$	$1$		$q-\zeta_{10}^{3}q^{2}+\zeta_{10}q^{3}-\zeta_{10}q^{4}+\zeta_{10}q^{5}+\cdots$
2100.1.bs.c	$2100$	$1$	2100.bs	2100.as	$10$	$4$	$1$	$1.048$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$1$	$-1$	$1$	$4$	$1$		$q+\zeta_{10}^{3}q^{2}-\zeta_{10}q^{3}-\zeta_{10}q^{4}+\zeta_{10}q^{5}+\cdots$
2100.1.bs.d	$2100$	$1$	2100.bs	2100.as	$10$	$4$	$1$	$1.048$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$1$	$1$	$-1$	$-4$	$1$		$q+\zeta_{10}^{3}q^{2}+\zeta_{10}q^{3}-\zeta_{10}q^{4}-\zeta_{10}q^{5}+\cdots$
2268.1.s.a	$2268$	$1$	2268.s	252.s	$6$	$2$	$1$	$1.132$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-21}) $	None		$4$	$0$	$-1$	$0$	$-1$	$1$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots$

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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.