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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 1498 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
56.1.h.a	$56$	$1$	56.h	56.h	$2$	$1$	$1$	$0.028$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-14}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q-q^{2}+q^{4}-q^{7}-q^{8}-q^{9}+q^{14}+\cdots$
63.1.d.a	$63$	$1$	63.d	7.b	$2$	$1$	$1$	$0.031$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-7}) $	$\Q(\sqrt{21}) $	✓	$4$	$0$	$0$	$0$	$0$	$-1$	$1$		$q-q^{4}-q^{7}+q^{16}+q^{25}+q^{28}-2q^{37}+\cdots$
77.1.j.a	$77$	$1$	77.j	77.j	$10$	$4$	$1$	$0.038$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$	$1$		$q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots$
112.1.l.a	$112$	$1$	112.l	112.l	$4$	$2$	$1$	$0.056$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{2}-q^{4}+iq^{7}-iq^{8}-iq^{9}+\cdots$
161.1.l.a	$161$	$1$	161.l	161.l	$22$	$10$	$1$	$0.080$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$	$1$		$q+(-\zeta_{22}+\zeta_{22}^{8})q^{2}+(\zeta_{22}^{2}-\zeta_{22}^{5}+\cdots)q^{4}+\cdots$
175.1.c.a	$175$	$1$	175.c	35.c	$2$	$2$	$2$	$0.087$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}+iq^{7}-iq^{8}-q^{9}-q^{11}+\cdots$
175.1.d.a	$175$	$1$	175.d	7.b	$2$	$1$	$1$	$0.087$	$\Q$	$D_{3}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$1$	$1$		$q-q^{2}+q^{7}+q^{8}+q^{9}-q^{11}-q^{14}+\cdots$
175.1.d.b	$175$	$1$	175.d	7.b	$2$	$1$	$1$	$0.087$	$\Q$	$D_{3}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$-1$	$1$		$q+q^{2}-q^{7}-q^{8}+q^{9}-q^{11}-q^{14}+\cdots$
196.1.c.a	$196$	$1$	196.c	4.b	$2$	$1$	$1$	$0.098$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-7}) $	$\Q(\sqrt{7}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{18}+\cdots$
196.1.g.a	$196$	$1$	196.g	28.g	$6$	$2$	$1$	$0.098$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-7}) $	$\Q(\sqrt{7}) $		$8$	$0$	$1$	$0$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
203.1.c.a	$203$	$1$	203.c	203.c	$2$	$1$	$1$	$0.101$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-203}) $	$\Q(\sqrt{29}) $	✓	$4$	$0$	$0$	$0$	$0$	$-1$	$1$		$q+q^{4}-q^{7}-q^{9}+q^{16}-2q^{23}+q^{25}+\cdots$
203.1.n.a	$203$	$1$	203.n	203.n	$14$	$6$	$1$	$0.101$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$	$1$		$q+(-\zeta_{14}^{3}+\zeta_{14}^{6})q^{2}+(\zeta_{14}^{2}-\zeta_{14}^{5}+\cdots)q^{4}+\cdots$
203.1.o.a	$203$	$1$	203.o	203.o	$14$	$6$	$1$	$0.101$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$1$	$1$		$q+(\zeta_{14}^{5}+\zeta_{14}^{6})q^{2}+(-\zeta_{14}^{3}-\zeta_{14}^{4}+\cdots)q^{4}+\cdots$
224.1.h.a	$224$	$1$	224.h	56.h	$2$	$1$	$1$	$0.112$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-14}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$0$	$0$	$0$	$1$	$1$		$q+q^{7}-q^{9}-2q^{23}-q^{25}+q^{49}+\cdots$
224.1.v.a	$224$	$1$	224.v	224.v	$8$	$4$	$1$	$0.112$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}q^{7}+\zeta_{8}^{3}q^{8}+\cdots$
252.1.h.a	$252$	$1$	252.h	84.h	$2$	$4$	$4$	$0.126$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{2}q^{7}-\zeta_{8}^{3}q^{8}+\cdots$
259.1.b.a	$259$	$1$	259.b	259.b	$2$	$1$	$1$	$0.129$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-259}) $	$\Q(\sqrt{37}) $	✓	$4$	$0$	$0$	$0$	$0$	$-1$	$1$		$q+q^{4}-q^{7}+q^{9}-2q^{11}+q^{16}-q^{25}+\cdots$
259.1.n.a	$259$	$1$	259.n	259.n	$6$	$2$	$1$	$0.129$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$1$	$0$	$0$	$-1$	$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{7}+q^{8}-\zeta_{6}q^{9}-q^{11}+\cdots$
259.1.s.a	$259$	$1$	259.s	259.s	$6$	$2$	$1$	$0.129$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-3$	$0$	$0$	$1$	$1$		$q+(-1-\zeta_{6})q^{2}+(1+\zeta_{6}+\zeta_{6}^{2})q^{4}+\cdots$
259.1.bi.a	$259$	$1$	259.bi	259.ai	$18$	$6$	$1$	$0.129$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}^{3}+\zeta_{18}^{4})q^{2}+(\zeta_{18}^{6}-\zeta_{18}^{7}+\cdots)q^{4}+\cdots$
259.1.bo.a	$259$	$1$	259.bo	259.ao	$18$	$6$	$1$	$0.129$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{3}-\zeta_{18}^{7})q^{2}+(\zeta_{18}-\zeta_{18}^{5}+\cdots)q^{4}+\cdots$
301.1.t.a	$301$	$1$	301.t	301.t	$6$	$2$	$1$	$0.150$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$	$1$		$q-q^{2}-\zeta_{6}q^{7}+q^{8}-\zeta_{6}q^{9}+q^{11}+\cdots$
301.1.v.a	$301$	$1$	301.v	301.v	$14$	$6$	$1$	$0.150$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$6$	$1$		$q+(-\zeta_{14}-\zeta_{14}^{3})q^{2}+(\zeta_{14}^{2}+\zeta_{14}^{4}+\cdots)q^{4}+\cdots$
301.1.bc.a	$301$	$1$	301.bc	301.ac	$42$	$12$	$1$	$0.150$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$-6$	$1$		$q+(\zeta_{42}^{16}+\zeta_{42}^{20})q^{2}+(-\zeta_{42}^{11}+\cdots)q^{4}+\cdots$
308.1.g.a	$308$	$1$	308.g	308.g	$2$	$1$	$1$	$0.154$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-77}) $	$\Q(\sqrt{11}) $	✓	$4$	$0$	$-1$	$0$	$0$	$1$	$1$		$q-q^{2}+q^{4}+q^{7}-q^{8}-q^{9}+q^{11}+\cdots$
308.1.g.b	$308$	$1$	308.g	308.g	$2$	$1$	$1$	$0.154$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-77}) $	$\Q(\sqrt{11}) $	✓	$4$	$0$	$1$	$0$	$0$	$-1$	$1$		$q+q^{2}+q^{4}-q^{7}+q^{8}-q^{9}-q^{11}+\cdots$
308.1.s.a	$308$	$1$	308.s	308.s	$10$	$4$	$1$	$0.154$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-1$	$0$	$0$	$1$	$1$		$q+\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}-\zeta_{10}^{2}q^{7}+\cdots$
308.1.s.b	$308$	$1$	308.s	308.s	$10$	$4$	$1$	$0.154$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$1$	$0$	$0$	$-1$	$1$		$q+\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{2}q^{7}-\zeta_{10}^{4}q^{8}+\cdots$
343.1.b.a	$343$	$1$	343.b	7.b	$2$	$3$	$3$	$0.171$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{2})q^{8}+\cdots$
343.1.d.a	$343$	$1$	343.d	7.d	$6$	$6$	$3$	$0.171$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{2}+(-1+\cdots)q^{4}+\cdots$
371.1.c.a	$371$	$1$	371.c	371.c	$2$	$1$	$1$	$0.185$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-371}) $	$\Q(\sqrt{53}) $	✓	$4$	$0$	$0$	$0$	$0$	$1$	$1$		$q+q^{4}+q^{7}-q^{9}-2q^{11}+q^{16}-q^{25}+\cdots$
371.1.n.a	$371$	$1$	371.n	371.n	$26$	$12$	$1$	$0.185$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$	$1$		$q+(-\zeta_{26}+\zeta_{26}^{6})q^{2}+(\zeta_{26}^{2}-\zeta_{26}^{7}+\cdots)q^{4}+\cdots$
371.1.o.a	$371$	$1$	371.o	371.o	$26$	$12$	$1$	$0.185$	$\Q(\zeta_{26})$	$D_{26}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$-1$	$1$		$q+(-\zeta_{26}^{8}-\zeta_{26}^{9})q^{2}+(-\zeta_{26}^{3}-\zeta_{26}^{4}+\cdots)q^{4}+\cdots$
7.3.b.a	$7$	$3$	7.b	7.b	$2$	$1$	$1$	$0.191$	$\Q$	$_{}$	$\Q(\sqrt{-7}) $	None	✓	$2$	$0$	$-3$	$0$	$0$	$-7$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-3q^{2}+5q^{4}-7q^{7}-3q^{8}+9q^{9}+\cdots$
392.1.g.a	$392$	$1$	392.g	8.d	$2$	$1$	$1$	$0.196$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{14}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}-q^{9}-2q^{11}+q^{16}+\cdots$
392.1.j.a	$392$	$1$	392.j	56.j	$6$	$2$	$1$	$0.196$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-14}) $	$\Q(\sqrt{2}) $		$8$	$0$	$1$	$0$	$0$	$0$	$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{8}+\zeta_{6}q^{9}-\zeta_{6}q^{16}+\cdots$
392.1.k.a	$392$	$1$	392.k	56.k	$6$	$2$	$1$	$0.196$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{14}) $		$8$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+q^{8}+\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}+\cdots$
441.1.b.a	$441$	$1$	441.b	3.b	$2$	$2$	$2$	$0.220$	$\Q(\sqrt{-2}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta q^{2}-q^{4}-\beta q^{11}-q^{16}-2q^{22}+\cdots$
441.1.m.a	$441$	$1$	441.m	7.d	$6$	$2$	$1$	$0.220$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-7}) $	$\Q(\sqrt{21}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{4}-\zeta_{6}q^{16}+\zeta_{6}^{2}q^{25}+\zeta_{6}q^{37}+\cdots$
441.1.q.a	$441$	$1$	441.q	21.h	$6$	$4$	$2$	$0.220$	$\Q(\sqrt{-2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{3})q^{11}+\cdots$
28.2.d.a	$28$	$2$	28.d	28.d	$2$	$2$	$2$	$0.224$	$\Q(\sqrt{-7}) $	$_{}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{2}+(-2+\beta )q^{4}+(-1+2\beta )q^{7}+\cdots$
448.1.l.a	$448$	$1$	448.l	112.l	$4$	$2$	$1$	$0.224$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{7}-iq^{9}+(1+i)q^{11}+iq^{25}+\cdots$
448.1.bf.a	$448$	$1$	448.bf	448.af	$16$	$8$	$1$	$0.224$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{16}q^{2}+\zeta_{16}^{2}q^{4}+\zeta_{16}^{5}q^{7}-\zeta_{16}^{3}q^{8}+\cdots$
469.1.k.a	$469$	$1$	469.k	469.k	$6$	$2$	$1$	$0.234$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$	$1$		$q+\zeta_{6}^{2}q^{2}-3\zeta_{6}q^{4}-\zeta_{6}q^{7}-2q^{8}+\cdots$
469.1.v.a	$469$	$1$	469.v	469.v	$22$	$10$	$1$	$0.234$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$	$1$		$q+(-\zeta_{22}^{9}+\zeta_{22}^{10})q^{2}+(-\zeta_{22}^{7}+\cdots)q^{4}+\cdots$
469.1.bl.a	$469$	$1$	469.bl	469.al	$66$	$20$	$1$	$0.234$	$\Q(\zeta_{33})$	$D_{33}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$1$	$1$		$q+(\zeta_{66}^{10}+\zeta_{66}^{16})q^{2}+(\zeta_{66}^{20}+\zeta_{66}^{26}+\cdots)q^{4}+\cdots$
497.1.l.a	$497$	$1$	497.l	497.l	$10$	$4$	$1$	$0.248$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$3$	$0$	$0$	$-1$	$1$		$q+(1-\zeta_{10}^{3})q^{2}+(1-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots$
497.1.o.a	$497$	$1$	497.o	497.o	$14$	$6$	$1$	$0.248$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$	$1$		$q+(-\zeta_{14}+\zeta_{14}^{2})q^{2}+(\zeta_{14}^{2}-\zeta_{14}^{3}+\cdots)q^{4}+\cdots$
497.1.ba.a	$497$	$1$	497.ba	497.aa	$70$	$24$	$1$	$0.248$	$\Q(\zeta_{35})$	$D_{35}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-3$	$0$	$0$	$1$	$1$		$q+(\zeta_{70}^{12}+\zeta_{70}^{20})q^{2}+(-\zeta_{70}^{5}+\zeta_{70}^{24}+\cdots)q^{4}+\cdots$
504.1.e.a	$504$	$1$	504.e	168.e	$2$	$4$	$4$	$0.252$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{2}q^{7}-\zeta_{8}^{3}q^{8}+\cdots$

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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.