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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 65 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
404.1.o.a	$404$	$1$	404.o	404.o	$50$	$20$	$1$	$0.202$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{50}^{4}q^{2}+\zeta_{50}^{8}q^{4}+(\zeta_{50}^{18}+\zeta_{50}^{24}+\cdots)q^{5}+\cdots$
453.1.t.a	$453$	$1$	453.t	453.t	$50$	$20$	$1$	$0.226$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{50}^{11}q^{3}-\zeta_{50}^{15}q^{4}+(\zeta_{50}^{6}-\zeta_{50}^{23}+\cdots)q^{7}+\cdots$
479.1.b.b	$479$	$1$	479.b	479.b	$2$	$10$	$10$	$0.239$	$\Q(\zeta_{50})^+$	$D_{25}$	$\Q(\sqrt{-479}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}-\beta _{9}q^{5}+\cdots$
500.1.p.a	$500$	$1$	500.p	500.p	$50$	$20$	$1$	$0.250$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{50}^{13}q^{2}-\zeta_{50}q^{4}-\zeta_{50}^{9}q^{5}+\cdots$
599.1.b.b	$599$	$1$	599.b	599.b	$2$	$10$	$10$	$0.299$	$\Q(\zeta_{50})^+$	$D_{25}$	$\Q(\sqrt{-599}) $	None	✓	$2$	$0$	$0$	$0$	$-5$	$0$	$1$		$q-\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
869.1.j.a	$869$	$1$	869.j	869.j	$10$	$20$	$5$	$0.434$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{2}+(-\zeta_{50}^{5}+\cdots)q^{4}+\cdots$
1057.1.bq.a	$1057$	$1$	1057.bq	1057.aq	$50$	$20$	$1$	$0.528$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{50}^{12}-\zeta_{50}^{23})q^{2}+(\zeta_{50}^{10}-\zeta_{50}^{21}+\cdots)q^{4}+\cdots$
1367.1.b.b	$1367$	$1$	1367.b	1367.b	$2$	$10$	$10$	$0.682$	$\Q(\zeta_{50})^+$	$D_{25}$	$\Q(\sqrt{-1367}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{2})q^{4}+(\beta _{6}+\cdots)q^{6}+\cdots$
1375.1.ch.a	$1375$	$1$	1375.ch	1375.bh	$50$	$20$	$1$	$0.686$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$-5$	$0$	$1$		$q+(\zeta_{50}^{4}+\zeta_{50}^{18})q^{3}-\zeta_{50}^{21}q^{4}+\cdots$
1397.1.l.a	$1397$	$1$	1397.l	1397.l	$10$	$20$	$5$	$0.697$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-127}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{50}^{16}-\zeta_{50}^{19})q^{2}+(-\zeta_{50}^{7}+\zeta_{50}^{10}+\cdots)q^{4}+\cdots$
1441.1.u.a	$1441$	$1$	1441.u	1441.u	$10$	$20$	$5$	$0.719$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{3}+\zeta_{50}^{10}q^{4}+\cdots$
1604.1.t.a	$1604$	$1$	1604.t	1604.t	$50$	$20$	$1$	$0.801$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-5$	$0$	$1$		$q-\zeta_{50}^{3}q^{2}+\zeta_{50}^{6}q^{4}+(\zeta_{50}^{18}+\zeta_{50}^{20}+\cdots)q^{5}+\cdots$
1799.1.d.c	$1799$	$1$	1799.d	1799.d	$2$	$10$	$10$	$0.898$	$\Q(\zeta_{50})^+$	$D_{25}$	$\Q(\sqrt{-1799}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$10$	$1$		$q+(\beta _{1}-\beta _{4}-\beta _{6}+\beta _{9})q^{2}-\beta _{1}q^{3}+\cdots$
1799.1.d.d	$1799$	$1$	1799.d	1799.d	$2$	$10$	$10$	$0.898$	$\Q(\zeta_{50})^+$	$D_{25}$	$\Q(\sqrt{-1799}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$-10$	$1$		$q+(\beta _{1}-\beta _{4}-\beta _{6}+\beta _{9})q^{2}+\beta _{1}q^{3}+\cdots$
1803.1.be.a	$1803$	$1$	1803.be	1803.ae	$50$	$20$	$1$	$0.900$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{50}^{13}q^{3}+\zeta_{50}^{8}q^{4}+(-\zeta_{50}^{3}+\cdots)q^{7}+\cdots$
1919.1.bf.a	$1919$	$1$	1919.bf	1919.af	$50$	$20$	$1$	$0.958$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{50}^{6}q^{4}+(\zeta_{50}^{2}-\zeta_{50}^{17})q^{5}+(-\zeta_{50}^{13}+\cdots)q^{7}+\cdots$
1975.1.l.a	$1975$	$1$	1975.l	1975.l	$10$	$20$	$5$	$0.986$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{2}+(-\zeta_{50}^{5}+\cdots)q^{4}+\cdots$
2008.1.w.a	$2008$	$1$	2008.w	2008.w	$50$	$20$	$1$	$1.002$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-5$	$0$	$0$	$0$	$1$		$q-\zeta_{50}^{5}q^{2}+(\zeta_{50}^{2}+\zeta_{50}^{4})q^{3}+\zeta_{50}^{10}q^{4}+\cdots$
2020.1.bu.a	$2020$	$1$	2020.bu	2020.au	$50$	$20$	$1$	$1.008$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$-5$	$0$	$-5$	$1$		$q-\zeta_{50}^{9}q^{2}+(-\zeta_{50}^{7}+\zeta_{50}^{10})q^{3}+\cdots$
2020.1.bu.b	$2020$	$1$	2020.bu	2020.au	$50$	$20$	$1$	$1.008$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$5$	$0$	$5$	$1$		$q+\zeta_{50}^{9}q^{2}+(\zeta_{50}^{7}-\zeta_{50}^{10})q^{3}+\zeta_{50}^{18}q^{4}+\cdots$
2253.1.t.a	$2253$	$1$	2253.t	2253.t	$50$	$20$	$1$	$1.124$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{50}^{8}q^{3}+\zeta_{50}^{6}q^{4}+(\zeta_{50}^{18}-\zeta_{50}^{23}+\cdots)q^{7}+\cdots$
2265.1.bt.a	$2265$	$1$	2265.bt	2265.at	$50$	$20$	$1$	$1.130$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{50}^{8}+\zeta_{50}^{22})q^{2}+\zeta_{50}^{2}q^{3}+(-\zeta_{50}^{5}+\cdots)q^{4}+\cdots$
2265.1.bt.b	$2265$	$1$	2265.bt	2265.at	$50$	$20$	$1$	$1.130$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{50}^{8}-\zeta_{50}^{22})q^{2}-\zeta_{50}^{2}q^{3}+\cdots$
2323.1.u.a	$2323$	$1$	2323.u	2323.u	$50$	$20$	$1$	$1.159$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{50}^{12}+\zeta_{50}^{14})q^{2}+(\zeta_{50}^{8}-\zeta_{50}^{11}+\cdots)q^{3}+\cdots$
2375.1.be.a	$2375$	$1$	2375.be	2375.ae	$50$	$20$	$1$	$1.185$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{50}^{6}q^{4}+\zeta_{50}^{22}q^{5}+(-\zeta_{50}^{13}+\cdots)q^{7}+\cdots$
2404.1.bd.a	$2404$	$1$	2404.bd	2404.ad	$50$	$20$	$1$	$1.200$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{50}^{12}q^{2}+\zeta_{50}^{24}q^{4}+(\zeta_{50}^{6}-\zeta_{50}^{19}+\cdots)q^{5}+\cdots$
2424.1.cj.a	$2424$	$1$	2424.cj	2424.bj	$50$	$20$	$1$	$1.210$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{50}^{9}q^{2}-\zeta_{50}^{21}q^{3}+\zeta_{50}^{18}q^{4}+\cdots$
2424.1.cj.b	$2424$	$1$	2424.cj	2424.bj	$50$	$20$	$1$	$1.210$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{50}^{9}q^{2}+\zeta_{50}^{21}q^{3}+\zeta_{50}^{18}q^{4}+\cdots$
2449.1.x.a	$2449$	$1$	2449.x	2449.x	$10$	$20$	$5$	$1.222$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{2}+(-\zeta_{50}^{5}+\cdots)q^{4}+\cdots$
2497.1.h.a	$2497$	$1$	2497.h	2497.h	$10$	$20$	$5$	$1.246$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-227}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{50}^{16}-\zeta_{50}^{19})q^{3}+\zeta_{50}^{20}q^{4}+\cdots$
2500.1.n.a	$2500$	$1$	2500.n	500.n	$50$	$40$	$2$	$1.248$	$\Q(\zeta_{100})$	$D_{25}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{100}q^{2}+\zeta_{100}^{2}q^{4}-\zeta_{100}^{3}q^{8}+\zeta_{100}^{14}q^{9}+\cdots$
2500.1.p.a	$2500$	$1$	2500.p	500.p	$50$	$20$	$1$	$1.248$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{50}^{3}q^{2}+\zeta_{50}^{6}q^{4}+\zeta_{50}^{9}q^{8}+\cdots$
2629.1.g.a	$2629$	$1$	2629.g	2629.g	$10$	$20$	$5$	$1.312$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-239}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{50}^{16}-\zeta_{50}^{19})q^{2}+(-\zeta_{50}^{9}-\zeta_{50}^{21}+\cdots)q^{3}+\cdots$
2761.1.br.a	$2761$	$1$	2761.br	2761.ar	$50$	$20$	$1$	$1.378$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-5$	$0$	$0$	$1$		$q+(\zeta_{50}^{10}+\zeta_{50}^{16})q^{3}+\zeta_{50}^{10}q^{4}+\cdots$
2804.1.v.a	$2804$	$1$	2804.v	2804.v	$50$	$20$	$1$	$1.399$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{50}^{23}q^{2}-\zeta_{50}^{21}q^{4}+(-\zeta_{50}^{11}+\cdots)q^{5}+\cdots$
2807.1.bi.a	$2807$	$1$	2807.bi	2807.ai	$50$	$20$	$1$	$1.401$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-5$	$0$	$0$	$0$	$1$		$q+(\zeta_{50}^{14}-\zeta_{50}^{15})q^{2}+(-\zeta_{50}^{3}+\zeta_{50}^{4}+\cdots)q^{4}+\cdots$
2867.1.l.a	$2867$	$1$	2867.l	2867.l	$10$	$20$	$5$	$1.431$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{50}^{16}-\zeta_{50}^{19})q^{2}+(-\zeta_{50}^{17}+\cdots)q^{3}+\cdots$
2887.1.b.b	$2887$	$1$	2887.b	2887.b	$2$	$10$	$10$	$1.441$	$\Q(\zeta_{50})^+$	$D_{25}$	$\Q(\sqrt{-2887}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{9}q^{7}+(-\beta _{1}+\cdots)q^{8}+\cdots$
2975.1.bl.a	$2975$	$1$	2975.bl	2975.al	$10$	$20$	$5$	$1.485$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$0$	$0$	$0$	$-20$	$1$		$q+(\zeta_{50}^{16}+\zeta_{50}^{24})q^{2}+(\zeta_{50}^{9}+\zeta_{50}^{21}+\cdots)q^{3}+\cdots$
2975.1.bl.b	$2975$	$1$	2975.bl	2975.al	$10$	$20$	$5$	$1.485$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$0$	$0$	$0$	$20$	$1$		$q+(\zeta_{50}^{16}+\zeta_{50}^{24})q^{2}+(-\zeta_{50}^{9}-\zeta_{50}^{21}+\cdots)q^{3}+\cdots$
3000.1.ca.a	$3000$	$1$	3000.ca	3000.ba	$50$	$20$	$1$	$1.497$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{50}^{8}q^{2}+\zeta_{50}^{6}q^{3}+\zeta_{50}^{16}q^{4}+\cdots$
3000.1.ca.b	$3000$	$1$	3000.ca	3000.ba	$50$	$20$	$1$	$1.497$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{50}^{8}q^{2}-\zeta_{50}^{6}q^{3}+\zeta_{50}^{16}q^{4}+\cdots$
3131.1.dn.a	$3131$	$1$	3131.dn	3131.cn	$50$	$20$	$1$	$1.563$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{50}^{7}-\zeta_{50}^{11})q^{2}+(\zeta_{50}^{14}+\zeta_{50}^{18}+\cdots)q^{4}+\cdots$
3153.1.ba.a	$3153$	$1$	3153.ba	3153.aa	$50$	$20$	$1$	$1.574$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-5$	$0$	$0$	$1$		$q+\zeta_{50}^{20}q^{3}-\zeta_{50}^{7}q^{4}+(\zeta_{50}^{2}+\zeta_{50}^{14}+\cdots)q^{7}+\cdots$
3208.1.bo.a	$3208$	$1$	3208.bo	3208.ao	$50$	$20$	$1$	$1.601$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-5$	$0$	$0$	$1$		$q-\zeta_{50}^{3}q^{2}+(-\zeta_{50}^{11}+\zeta_{50}^{20})q^{3}+\cdots$
3215.1.d.c	$3215$	$1$	3215.d	3215.d	$2$	$10$	$10$	$1.604$	$\Q(\zeta_{50})^+$	$D_{25}$	$\Q(\sqrt{-3215}) $	None	✓	$2$	$0$	$0$	$0$	$-10$	$0$	$1$		$q+\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
3215.1.d.d	$3215$	$1$	3215.d	3215.d	$2$	$10$	$10$	$1.604$	$\Q(\zeta_{50})^+$	$D_{25}$	$\Q(\sqrt{-3215}) $	None	✓	$2$	$0$	$0$	$0$	$10$	$0$	$1$		$q-\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
3256.1.br.a	$3256$	$1$	3256.br	3256.ar	$10$	$20$	$5$	$1.625$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-74}) $	None		$4$	$0$	$-5$	$0$	$0$	$0$	$1$		$q-\zeta_{50}^{5}q^{2}+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{3}+\cdots$
3256.1.br.b	$3256$	$1$	3256.br	3256.ar	$10$	$20$	$5$	$1.625$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-74}) $	None		$4$	$0$	$5$	$0$	$0$	$0$	$1$		$q+\zeta_{50}^{5}q^{2}+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{3}+\cdots$
3275.1.x.a	$3275$	$1$	3275.x	3275.x	$10$	$20$	$5$	$1.634$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{3}-\zeta_{50}^{15}q^{4}+\cdots$

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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.