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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 173 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
208.1.c.a	$208$	$1$	208.c	52.b	$2$	$1$	$1$	$0.104$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-13}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{9}-q^{13}-2q^{17}+q^{25}-2q^{29}+\cdots$
364.1.bl.a	$364$	$1$	364.bl	364.al	$6$	$2$	$1$	$0.182$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{7}+q^{8}-\zeta_{6}q^{9}+\cdots$
364.1.bl.b	$364$	$1$	364.bl	364.al	$6$	$2$	$1$	$0.182$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$1$	$0$	$0$	$1$	$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{7}-q^{8}-\zeta_{6}q^{9}+\cdots$
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}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}-2q^{11}-q^{13}+q^{16}+\cdots$
572.1.ba.a	$572$	$1$	572.ba	572.aa	$10$	$4$	$1$	$0.285$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$-1$	$0$	$0$	$-2$	$1$		$q+\zeta_{10}^{2}q^{2}+\zeta_{10}^{4}q^{4}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{7}+\cdots$
572.1.ba.b	$572$	$1$	572.ba	572.aa	$10$	$4$	$1$	$0.285$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$1$	$0$	$0$	$2$	$1$		$q-\zeta_{10}^{2}q^{2}+\zeta_{10}^{4}q^{4}+(\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{7}+\cdots$
832.1.c.a	$832$	$1$	832.c	52.b	$2$	$1$	$1$	$0.415$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-13}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{9}+q^{13}-2q^{17}+q^{25}+2q^{29}+\cdots$
884.1.h.a	$884$	$1$	884.h	884.h	$2$	$1$	$1$	$0.441$	$\Q$	$D_{2}$	$\Q(\sqrt{-13}) $, $\Q(\sqrt{-221}) $	$\Q(\sqrt{17}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}-q^{9}+q^{13}+q^{16}+\cdots$
884.1.h.b	$884$	$1$	884.h	884.h	$2$	$1$	$1$	$0.441$	$\Q$	$D_{2}$	$\Q(\sqrt{-13}) $, $\Q(\sqrt{-221}) $	$\Q(\sqrt{17}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}-q^{9}+q^{13}+q^{16}+\cdots$
884.1.n.a	$884$	$1$	884.n	884.n	$4$	$2$	$1$	$0.441$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-iq^{2}-q^{4}+(-1+i)q^{7}+iq^{8}+\cdots$
884.1.n.b	$884$	$1$	884.n	884.n	$4$	$2$	$1$	$0.441$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+iq^{2}-q^{4}+(1-i)q^{7}-iq^{8}+iq^{9}+\cdots$
884.1.bg.c	$884$	$1$	884.bg	884.ag	$8$	$4$	$1$	$0.441$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(\zeta_{8}-\zeta_{8}^{2})q^{7}+\cdots$
884.1.bg.d	$884$	$1$	884.bg	884.ag	$8$	$4$	$1$	$0.441$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{7}+\cdots$
988.1.bm.a	$988$	$1$	988.bm	988.am	$6$	$2$	$1$	$0.493$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$-1$	$0$	$0$	$4$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+q^{7}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
988.1.bm.b	$988$	$1$	988.bm	988.am	$6$	$2$	$1$	$0.493$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$1$	$0$	$0$	$-4$	$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{7}-q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
988.1.cr.a	$988$	$1$	988.cr	988.br	$18$	$6$	$1$	$0.493$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$0$	$0$	$0$	$-3$	$1$		$q-\zeta_{18}^{8}q^{2}-\zeta_{18}^{7}q^{4}-\zeta_{18}^{3}q^{7}+\cdots$
988.1.cr.b	$988$	$1$	988.cr	988.br	$18$	$6$	$1$	$0.493$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$0$	$0$	$0$	$3$	$1$		$q+\zeta_{18}^{8}q^{2}-\zeta_{18}^{7}q^{4}+\zeta_{18}^{3}q^{7}+\cdots$
1300.1.e.a	$1300$	$1$	1300.e	52.b	$2$	$1$	$1$	$0.649$	$\Q$	$D_{3}$	$\Q(\sqrt{-13}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$1$	$1$		$q-q^{2}+q^{4}+q^{7}-q^{8}+q^{9}-q^{11}+\cdots$
1300.1.e.b	$1300$	$1$	1300.e	52.b	$2$	$1$	$1$	$0.649$	$\Q$	$D_{3}$	$\Q(\sqrt{-13}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$1$	$1$		$q-q^{2}+q^{4}+q^{7}-q^{8}+q^{9}+q^{11}+\cdots$
1300.1.e.c	$1300$	$1$	1300.e	52.b	$2$	$1$	$1$	$0.649$	$\Q$	$D_{3}$	$\Q(\sqrt{-13}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$-1$	$1$		$q+q^{2}+q^{4}-q^{7}+q^{8}+q^{9}-q^{11}+\cdots$
1300.1.e.d	$1300$	$1$	1300.e	52.b	$2$	$1$	$1$	$0.649$	$\Q$	$D_{3}$	$\Q(\sqrt{-13}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$-1$	$1$		$q+q^{2}+q^{4}-q^{7}+q^{8}+q^{9}+q^{11}+\cdots$
1300.1.g.a	$1300$	$1$	1300.g	260.g	$2$	$2$	$2$	$0.649$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{2}-q^{4}-iq^{7}-iq^{8}-q^{9}-q^{11}+\cdots$
1300.1.g.b	$1300$	$1$	1300.g	260.g	$2$	$2$	$2$	$0.649$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{2}-q^{4}-iq^{7}-iq^{8}-q^{9}+q^{11}+\cdots$
1456.1.dj.a	$1456$	$1$	1456.dj	364.al	$6$	$4$	$2$	$0.727$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-13}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{7}+\zeta_{12}^{4}q^{9}+(-\zeta_{12}-\zeta_{12}^{3}+\cdots)q^{11}+\cdots$
1508.1.g.d	$1508$	$1$	1508.g	1508.g	$2$	$2$	$2$	$0.753$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-13}) $, $\Q(\sqrt{-29}) $	$\Q(\sqrt{377}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-q^{4}+iq^{8}-q^{9}+iq^{11}+\cdots$
1508.1.bq.c	$1508$	$1$	1508.bq	1508.aq	$14$	$12$	$2$	$0.753$	$\Q(\zeta_{28})$	$D_{14}$	$\Q(\sqrt{-13}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{28}^{13}q^{2}-\zeta_{28}^{12}q^{4}+(\zeta_{28}^{5}-\zeta_{28}^{13}+\cdots)q^{7}+\cdots$
1508.1.bu.a	$1508$	$1$	1508.bu	1508.au	$14$	$6$	$1$	$0.753$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$-1$	$0$	$0$	$-2$	$1$		$q-\zeta_{14}^{3}q^{2}+\zeta_{14}^{6}q^{4}+(-\zeta_{14}^{3}+\zeta_{14}^{6}+\cdots)q^{7}+\cdots$
1508.1.bu.b	$1508$	$1$	1508.bu	1508.au	$14$	$6$	$1$	$0.753$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$1$	$0$	$0$	$2$	$1$		$q+\zeta_{14}^{3}q^{2}+\zeta_{14}^{6}q^{4}+(\zeta_{14}^{3}-\zeta_{14}^{6}+\cdots)q^{7}+\cdots$
1612.1.bl.a	$1612$	$1$	1612.bl	1612.al	$6$	$2$	$1$	$0.804$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$	$1$		$q-q^{2}+q^{4}-\zeta_{6}q^{7}-q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
1612.1.bl.b	$1612$	$1$	1612.bl	1612.al	$6$	$2$	$1$	$0.804$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$2$	$0$	$0$	$1$	$1$		$q+q^{2}+q^{4}+\zeta_{6}q^{7}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
1612.1.bw.a	$1612$	$1$	1612.bw	1612.aw	$10$	$4$	$1$	$0.804$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$-1$	$0$	$0$	$3$	$1$		$q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+(1+\zeta_{10}^{4})q^{7}+\cdots$
1612.1.bw.b	$1612$	$1$	1612.bw	1612.aw	$10$	$4$	$1$	$0.804$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$1$	$0$	$0$	$-3$	$1$		$q+\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+(-1-\zeta_{10}^{4}+\cdots)q^{7}+\cdots$
1612.1.dj.a	$1612$	$1$	1612.dj	1612.cj	$30$	$8$	$1$	$0.804$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$-2$	$0$	$0$	$9$	$1$		$q+\zeta_{30}^{12}q^{2}-\zeta_{30}^{9}q^{4}+(1+\zeta_{30}^{8}+\cdots)q^{7}+\cdots$
1612.1.dj.b	$1612$	$1$	1612.dj	1612.cj	$30$	$8$	$1$	$0.804$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$2$	$0$	$0$	$-9$	$1$		$q-\zeta_{30}^{12}q^{2}-\zeta_{30}^{9}q^{4}+(-1-\zeta_{30}^{8}+\cdots)q^{7}+\cdots$
1664.1.h.e	$1664$	$1$	1664.h	104.h	$2$	$4$	$4$	$0.830$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-13}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2$		$q+(-\zeta_{8}+\zeta_{8}^{3})q^{7}-q^{9}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{11}+\cdots$
1872.1.i.a	$1872$	$1$	1872.i	52.b	$2$	$1$	$1$	$0.934$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-13}) $	$\Q(\sqrt{39}) $	✓	$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-2q^{7}+q^{13}+2q^{19}+q^{25}+2q^{31}+\cdots$
1872.1.i.b	$1872$	$1$	1872.i	52.b	$2$	$1$	$1$	$0.934$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-13}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{13}+2q^{17}+q^{25}+2q^{29}-q^{49}+\cdots$
1872.1.i.c	$1872$	$1$	1872.i	52.b	$2$	$1$	$1$	$0.934$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-13}) $	$\Q(\sqrt{39}) $	✓	$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+2q^{7}+q^{13}-2q^{19}+q^{25}-2q^{31}+\cdots$
2288.1.cq.a	$2288$	$1$	2288.cq	572.aa	$10$	$8$	$2$	$1.142$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-13}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{20}+\zeta_{20}^{7})q^{7}-\zeta_{20}^{2}q^{9}-\zeta_{20}^{9}q^{11}+\cdots$
2444.1.be.a	$2444$	$1$	2444.be	2444.ae	$46$	$22$	$1$	$1.220$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$-1$	$0$	$0$	$-2$	$1$		$q-\zeta_{46}^{13}q^{2}-\zeta_{46}^{3}q^{4}+(-\zeta_{46}^{17}+\cdots)q^{7}+\cdots$
2444.1.be.b	$2444$	$1$	2444.be	2444.ae	$46$	$22$	$1$	$1.220$	$\Q(\zeta_{46})$	$D_{23}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$1$	$0$	$0$	$2$	$1$		$q+\zeta_{46}^{13}q^{2}-\zeta_{46}^{3}q^{4}+(\zeta_{46}^{17}+\zeta_{46}^{19}+\cdots)q^{7}+\cdots$
2548.1.c.a	$2548$	$1$	2548.c	52.b	$2$	$1$	$1$	$1.272$	$\Q$	$D_{3}$	$\Q(\sqrt{-13}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}+q^{9}+q^{11}-q^{13}+\cdots$
2548.1.c.b	$2548$	$1$	2548.c	52.b	$2$	$1$	$1$	$1.272$	$\Q$	$D_{3}$	$\Q(\sqrt{-13}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}+q^{9}+q^{11}+q^{13}+\cdots$
2548.1.c.c	$2548$	$1$	2548.c	52.b	$2$	$1$	$1$	$1.272$	$\Q$	$D_{3}$	$\Q(\sqrt{-13}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}+q^{9}-q^{11}-q^{13}+\cdots$
2548.1.c.d	$2548$	$1$	2548.c	52.b	$2$	$1$	$1$	$1.272$	$\Q$	$D_{3}$	$\Q(\sqrt{-13}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}+q^{9}-q^{11}+q^{13}+\cdots$
2548.1.bl.a	$2548$	$1$	2548.bl	364.al	$6$	$2$	$1$	$1.272$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
2548.1.bl.b	$2548$	$1$	2548.bl	364.al	$6$	$2$	$1$	$1.272$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
2548.1.co.a	$2548$	$1$	2548.co	2548.bo	$14$	$6$	$1$	$1.272$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q-\zeta_{14}^{3}q^{2}+\zeta_{14}^{6}q^{4}-\zeta_{14}q^{7}+\zeta_{14}^{2}q^{8}+\cdots$
2548.1.co.b	$2548$	$1$	2548.co	2548.bo	$14$	$6$	$1$	$1.272$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-13}) $	None		$4$	$0$	$1$	$0$	$0$	$1$	$1$		$q+\zeta_{14}^{3}q^{2}+\zeta_{14}^{6}q^{4}+\zeta_{14}q^{7}-\zeta_{14}^{2}q^{8}+\cdots$

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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.