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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 312 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
39.1.d.a	$39$	$1$	39.d	39.d	$2$	$1$	$1$	$0.019$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}-q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots$
195.1.e.a	$195$	$1$	195.e	195.e	$2$	$4$	$4$	$0.097$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\cdots$
312.1.b.a	$312$	$1$	312.b	312.b	$2$	$4$	$4$	$0.156$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}-\zeta_{8}^{2}q^{3}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots$
351.1.d.a	$351$	$1$	351.d	39.d	$2$	$1$	$1$	$0.175$	$\Q$	$D_{3}$	$\Q(\sqrt{-39}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q-q^{2}-q^{5}+q^{8}+q^{10}+2q^{11}+q^{13}+\cdots$
351.1.d.b	$351$	$1$	351.d	39.d	$2$	$1$	$1$	$0.175$	$\Q$	$D_{3}$	$\Q(\sqrt{-39}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$0$	$1$		$q+q^{2}+q^{5}-q^{8}+q^{10}-2q^{11}+q^{13}+\cdots$
351.1.d.c	$351$	$1$	351.d	39.d	$2$	$2$	$2$	$0.175$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-39}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta q^{2}+2q^{4}+\beta q^{5}-\beta q^{8}-3q^{10}+\cdots$
429.1.v.a	$429$	$1$	429.v	429.v	$10$	$4$	$1$	$0.214$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$-3$	$-1$	$2$	$0$	$1$		$q+(-1+\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots$
429.1.v.b	$429$	$1$	429.v	429.v	$10$	$4$	$1$	$0.214$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$3$	$-1$	$-2$	$0$	$1$		$q+(1-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots$
429.1.v.c	$429$	$1$	429.v	429.v	$10$	$8$	$2$	$0.214$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$2$	$0$	$0$	$1$		$q+(-\zeta_{20}+\zeta_{20}^{5})q^{2}-\zeta_{20}^{4}q^{3}+(-1+\cdots)q^{4}+\cdots$
468.1.e.a	$468$	$1$	468.e	52.b	$2$	$1$	$1$	$0.234$	$\Q$	$D_{2}$	$\Q(\sqrt{-39}) $, $\Q(\sqrt{-13}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}+2q^{11}-q^{13}+q^{16}+\cdots$
468.1.e.b	$468$	$1$	468.e	52.b	$2$	$1$	$1$	$0.234$	$\Q$	$D_{2}$	$\Q(\sqrt{-39}) $, $\Q(\sqrt{-13}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}-2q^{11}-q^{13}+q^{16}+\cdots$
468.1.e.c	$468$	$1$	468.e	52.b	$2$	$2$	$2$	$0.234$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{39}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-q^{4}+iq^{5}+iq^{8}+2q^{10}+\cdots$
507.1.c.a	$507$	$1$	507.c	3.b	$2$	$1$	$1$	$0.253$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}+q^{4}+q^{9}-q^{12}+q^{16}+q^{25}+\cdots$
507.1.h.a	$507$	$1$	507.h	39.h	$6$	$2$	$1$	$0.253$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $		$8$	$0$	$0$	$1$	$0$	$0$	$1$		$q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{9}+q^{12}+\cdots$
507.1.i.a	$507$	$1$	507.i	39.i	$6$	$2$	$1$	$0.253$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $		$8$	$0$	$0$	$1$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{9}-q^{12}+\cdots$
585.1.o.a	$585$	$1$	585.o	65.h	$4$	$8$	$4$	$0.292$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{16}^{5}-\zeta_{16}^{7})q^{2}+(-\zeta_{16}^{2}+\zeta_{16}^{4}+\cdots)q^{4}+\cdots$
624.1.l.a	$624$	$1$	624.l	39.d	$2$	$1$	$1$	$0.311$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{9}-q^{13}-q^{25}+q^{27}-q^{39}+\cdots$
624.1.bi.a	$624$	$1$	624.bi	624.ai	$4$	$8$	$4$	$0.311$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}^{3}q^{2}-\zeta_{16}^{2}q^{3}+\zeta_{16}^{6}q^{4}+\cdots$
780.1.w.a	$780$	$1$	780.w	780.w	$4$	$8$	$4$	$0.389$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}^{3}q^{2}+\zeta_{16}^{2}q^{3}+\zeta_{16}^{6}q^{4}+\cdots$
780.1.w.b	$780$	$1$	780.w	780.w	$4$	$8$	$4$	$0.389$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}^{5}q^{2}+\zeta_{16}^{2}q^{3}-\zeta_{16}^{2}q^{4}+\cdots$
936.1.o.c	$936$	$1$	936.o	104.h	$2$	$4$	$4$	$0.467$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$
975.1.e.a	$975$	$1$	975.e	195.e	$2$	$2$	$2$	$0.487$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}+q^{4}-q^{9}-iq^{12}-iq^{13}+\cdots$
975.1.g.a	$975$	$1$	975.g	39.d	$2$	$1$	$1$	$0.487$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}-q^{4}+q^{9}-q^{12}+q^{13}+q^{16}+\cdots$
975.1.g.b	$975$	$1$	975.g	39.d	$2$	$2$	$2$	$0.487$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-39}) $	None	✓	$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-\beta q^{2}-q^{3}+q^{4}+\beta q^{6}+q^{9}-\beta q^{11}+\cdots$
975.1.g.c	$975$	$1$	975.g	39.d	$2$	$2$	$2$	$0.487$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-39}) $	None	✓	$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q-\beta q^{2}+q^{3}+q^{4}-\beta q^{6}+q^{9}+\beta q^{11}+\cdots$
975.1.bd.a	$975$	$1$	975.bd	975.ad	$10$	$4$	$1$	$0.487$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$-3$	$-1$	$1$	$0$	$1$		$q+(-1+\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots$
975.1.bd.b	$975$	$1$	975.bd	975.ad	$10$	$4$	$1$	$0.487$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$3$	$-1$	$-1$	$0$	$1$		$q+(1-\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots$
975.1.bd.c	$975$	$1$	975.bd	975.ad	$10$	$8$	$2$	$0.487$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$2$	$0$	$0$	$1$		$q+(-\zeta_{20}+\zeta_{20}^{5})q^{2}+\zeta_{20}^{6}q^{3}+(-1+\cdots)q^{4}+\cdots$
975.1.bi.a	$975$	$1$	975.bi	975.ai	$10$	$16$	$4$	$0.487$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{40}^{9}-\zeta_{40}^{15})q^{2}-\zeta_{40}^{14}q^{3}+\cdots$
1053.1.n.a	$1053$	$1$	1053.n	117.n	$6$	$2$	$1$	$0.526$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{5}-q^{8}+q^{10}-\zeta_{6}^{2}q^{11}+\cdots$
1053.1.n.b	$1053$	$1$	1053.n	117.n	$6$	$2$	$1$	$0.526$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{6}q^{4}+\zeta_{6}q^{13}+\zeta_{6}^{2}q^{16}-\zeta_{6}^{2}q^{25}+\cdots$
1053.1.n.c	$1053$	$1$	1053.n	117.n	$6$	$2$	$1$	$0.526$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$1$	$0$	$1$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{5}+q^{8}+q^{10}+\zeta_{6}^{2}q^{11}+\cdots$
1053.1.n.d	$1053$	$1$	1053.n	117.n	$6$	$4$	$2$	$0.526$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$3$		$q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}^{2}+\zeta_{12}^{4}+\cdots)q^{4}+\cdots$
1248.1.b.a	$1248$	$1$	1248.b	312.b	$2$	$4$	$4$	$0.623$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2$		$q-\zeta_{8}^{2}q^{3}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}-q^{9}+\cdots$
1248.1.cm.a	$1248$	$1$	1248.cm	1248.bm	$8$	$16$	$4$	$0.623$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{32}^{3}q^{2}+\zeta_{32}^{10}q^{3}+\zeta_{32}^{6}q^{4}+\cdots$
1287.1.g.c	$1287$	$1$	1287.g	143.d	$2$	$4$	$4$	$0.642$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+q^{4}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{5}+\cdots$
1287.1.bu.a	$1287$	$1$	1287.bu	143.l	$10$	$16$	$4$	$0.642$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{40}^{9}+\zeta_{40}^{15})q^{2}+(-\zeta_{40}^{4}-\zeta_{40}^{10}+\cdots)q^{4}+\cdots$
1404.1.e.a	$1404$	$1$	1404.e	52.b	$2$	$2$	$2$	$0.701$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{5}+\cdots$
1404.1.e.b	$1404$	$1$	1404.e	52.b	$2$	$2$	$2$	$0.701$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+(-\zeta_{6}-\zeta_{6}^{2})q^{5}+\cdots$
1404.1.e.c	$1404$	$1$	1404.e	52.b	$2$	$4$	$4$	$0.701$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}-\zeta_{12}^{3}q^{8}+\cdots$
1521.1.j.a	$1521$	$1$	1521.j	13.d	$4$	$2$	$1$	$0.759$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$-2$	$0$	$2$	$0$	$1$		$q+(-1-i)q^{2}+iq^{4}+(1+i)q^{5}-q^{8}+\cdots$
1521.1.j.c	$1521$	$1$	1521.j	13.d	$4$	$2$	$1$	$0.759$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$2$	$0$	$-2$	$0$	$1$		$q+(1+i)q^{2}+iq^{4}+(-1-i)q^{5}+q^{8}+\cdots$
1521.1.bd.a	$1521$	$1$	1521.bd	13.f	$12$	$4$	$1$	$0.759$	$\Q(\zeta_{12})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$-2$	$0$	$-4$	$0$	$1$		$q+(-\zeta_{12}^{2}-\zeta_{12}^{5})q^{2}-\zeta_{12}q^{4}+(-1+\cdots)q^{5}+\cdots$
1521.1.bd.d	$1521$	$1$	1521.bd	13.f	$12$	$4$	$1$	$0.759$	$\Q(\zeta_{12})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$2$	$0$	$4$	$0$	$1$		$q+(\zeta_{12}^{2}+\zeta_{12}^{5})q^{2}-\zeta_{12}q^{4}+(1+\zeta_{12}^{3}+\cdots)q^{5}+\cdots$
1560.1.y.a	$1560$	$1$	1560.y	1560.y	$2$	$1$	$1$	$0.779$	$\Q$	$D_{2}$	$\Q(\sqrt{-39}) $, $\Q(\sqrt{-390}) $	$\Q(\sqrt{10}) $	✓	$4$	$0$	$-1$	$-1$	$1$	$0$	$1$		$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots$
1560.1.y.b	$1560$	$1$	1560.y	1560.y	$2$	$1$	$1$	$0.779$	$\Q$	$D_{2}$	$\Q(\sqrt{-39}) $, $\Q(\sqrt{-390}) $	$\Q(\sqrt{10}) $	✓	$4$	$0$	$-1$	$1$	$1$	$0$	$1$		$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots$
1560.1.y.c	$1560$	$1$	1560.y	1560.y	$2$	$1$	$1$	$0.779$	$\Q$	$D_{2}$	$\Q(\sqrt{-39}) $, $\Q(\sqrt{-390}) $	$\Q(\sqrt{10}) $	✓	$4$	$0$	$1$	$-1$	$-1$	$0$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots$
1560.1.y.d	$1560$	$1$	1560.y	1560.y	$2$	$1$	$1$	$0.779$	$\Q$	$D_{2}$	$\Q(\sqrt{-39}) $, $\Q(\sqrt{-390}) $	$\Q(\sqrt{10}) $	✓	$4$	$0$	$1$	$1$	$-1$	$0$	$1$		$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
1560.1.y.e	$1560$	$1$	1560.y	1560.y	$2$	$2$	$2$	$0.779$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-39}) $, $\Q(\sqrt{-30}) $	$\Q(\sqrt{130}) $		$8$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-iq^{2}-q^{3}-q^{4}-iq^{5}+iq^{6}+iq^{8}+\cdots$
1560.1.y.f	$1560$	$1$	1560.y	1560.y	$2$	$2$	$2$	$0.779$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-39}) $, $\Q(\sqrt{-30}) $	$\Q(\sqrt{130}) $		$8$	$0$	$0$	$2$	$0$	$0$	$1$		$q-iq^{2}+q^{3}-q^{4}+iq^{5}-iq^{6}+iq^{8}+\cdots$

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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.