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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 452 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
239.1.b.c	$239$	$1$	239.b	239.b	$2$	$4$	$4$	$0.119$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-239}) $	None	✓	$2$	$0$	$1$	$-2$	$1$	$0$	$1$		$q+\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$
244.1.u.a	$244$	$1$	244.u	244.u	$30$	$8$	$1$	$0.122$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$-6$	$0$	$1$		$q+\zeta_{30}^{14}q^{2}-\zeta_{30}^{13}q^{4}+(\zeta_{30}^{6}+\zeta_{30}^{10}+\cdots)q^{5}+\cdots$
329.1.f.b	$329$	$1$	329.f	329.f	$6$	$8$	$4$	$0.164$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$-1$	$2$	$0$	$1$	$1$		$q+(\zeta_{30}^{8}+\zeta_{30}^{12})q^{2}+(-\zeta_{30}^{11}+\zeta_{30}^{14}+\cdots)q^{3}+\cdots$
341.1.by.a	$341$	$1$	341.by	341.ay	$30$	$8$	$1$	$0.170$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$-1$	$0$	$1$		$q+(\zeta_{30}^{2}+\zeta_{30}^{14})q^{3}-\zeta_{30}^{9}q^{4}+(\zeta_{30}^{8}+\cdots)q^{5}+\cdots$
372.1.be.a	$372$	$1$	372.be	93.o	$30$	$8$	$1$	$0.186$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$2$	$1$		$q-\zeta_{30}^{7}q^{3}+(\zeta_{30}^{4}-\zeta_{30}^{13})q^{7}+\zeta_{30}^{14}q^{9}+\cdots$
423.1.f.b	$423$	$1$	423.f	423.f	$6$	$8$	$4$	$0.211$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$2$	$-2$	$0$	$-1$	$1$		$q+(-\zeta_{30}^{11}+\zeta_{30}^{14})q^{2}+\zeta_{30}^{12}q^{3}+\cdots$
439.1.b.c	$439$	$1$	439.b	439.b	$2$	$4$	$4$	$0.219$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-439}) $	None	✓	$2$	$0$	$1$	$0$	$-2$	$1$	$1$		$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{3})q^{5}+\cdots$
465.1.bl.a	$465$	$1$	465.bl	465.al	$30$	$8$	$1$	$0.232$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-2$	$-1$	$4$	$0$	$1$		$q+(\zeta_{30}^{11}+\zeta_{30}^{13})q^{2}-\zeta_{30}^{8}q^{3}+\cdots$
465.1.bl.b	$465$	$1$	465.bl	465.al	$30$	$8$	$1$	$0.232$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$2$	$1$	$-4$	$0$	$1$		$q+(-\zeta_{30}^{11}-\zeta_{30}^{13})q^{2}+\zeta_{30}^{8}q^{3}+\cdots$
524.1.d.b	$524$	$1$	524.d	131.b	$2$	$4$	$4$	$0.262$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-131}) $	None	✓	$2$	$0$	$0$	$1$	$-2$	$1$	$1$		$q+\beta _{1}q^{3}+\beta _{3}q^{5}+(-\beta _{2}-\beta _{3})q^{7}+\cdots$
543.1.y.a	$543$	$1$	543.y	543.y	$30$	$8$	$1$	$0.271$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-4$	$1$		$q-\zeta_{30}^{11}q^{3}+\zeta_{30}^{2}q^{4}+(-\zeta_{30}^{3}+\cdots)q^{7}+\cdots$
651.1.cd.a	$651$	$1$	651.cd	651.bd	$30$	$8$	$1$	$0.325$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-2$	$0$	$1$	$1$		$q-\zeta_{30}^{9}q^{3}-\zeta_{30}^{7}q^{4}-\zeta_{30}q^{7}-\zeta_{30}^{3}q^{9}+\cdots$
651.1.ck.a	$651$	$1$	651.ck	651.bk	$30$	$8$	$1$	$0.325$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-2$	$1$		$q+\zeta_{30}^{8}q^{3}+\zeta_{30}^{4}q^{4}+\zeta_{30}^{6}q^{7}+\cdots$
671.1.d.e	$671$	$1$	671.d	671.d	$2$	$4$	$4$	$0.335$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-671}) $	None	✓	$2$	$0$	$-1$	$1$	$-2$	$4$	$1$		$q-\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
671.1.d.f	$671$	$1$	671.d	671.d	$2$	$4$	$4$	$0.335$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-671}) $	None	✓	$2$	$0$	$1$	$1$	$-2$	$-4$	$1$		$q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
713.1.j.b	$713$	$1$	713.j	713.j	$10$	$8$	$2$	$0.356$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$-3$	$2$	$0$	$0$	$1$		$q+(-\zeta_{30}^{5}-\zeta_{30}^{13})q^{2}+(\zeta_{30}^{4}+\zeta_{30}^{8}+\cdots)q^{3}+\cdots$
716.1.d.b	$716$	$1$	716.d	179.b	$2$	$4$	$4$	$0.357$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-179}) $	None	✓	$2$	$0$	$0$	$-2$	$1$	$0$	$1$		$q+\beta _{3}q^{3}+\beta _{1}q^{5}-\beta _{3}q^{9}+(1-\beta _{1}+\cdots)q^{13}+\cdots$
721.1.p.b	$721$	$1$	721.p	721.p	$6$	$8$	$4$	$0.360$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-103}) $	None		$4$	$0$	$-1$	$0$	$0$	$1$	$1$		$q+(\zeta_{30}^{8}+\zeta_{30}^{12})q^{2}+(-\zeta_{30}-\zeta_{30}^{5}+\cdots)q^{4}+\cdots$
724.1.x.a	$724$	$1$	724.x	724.x	$30$	$8$	$1$	$0.361$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$-3$	$0$	$1$		$q-\zeta_{30}^{7}q^{2}+\zeta_{30}^{14}q^{4}+(\zeta_{30}^{4}-\zeta_{30}^{5}+\cdots)q^{5}+\cdots$
732.1.bn.a	$732$	$1$	732.bn	183.t	$30$	$8$	$1$	$0.365$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-2$	$0$	$-3$	$1$		$q-\zeta_{30}^{3}q^{3}+(\zeta_{30}^{4}+\zeta_{30}^{10})q^{7}+\zeta_{30}^{6}q^{9}+\cdots$
744.1.cd.a	$744$	$1$	744.cd	744.bd	$30$	$8$	$1$	$0.371$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$-2$	$1$	$2$	$-6$	$1$		$q+\zeta_{30}^{6}q^{2}+\zeta_{30}^{14}q^{3}+\zeta_{30}^{12}q^{4}+\cdots$
744.1.cd.b	$744$	$1$	744.cd	744.bd	$30$	$8$	$1$	$0.371$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$2$	$-1$	$-2$	$-6$	$1$		$q-\zeta_{30}^{6}q^{2}-\zeta_{30}^{14}q^{3}+\zeta_{30}^{12}q^{4}+\cdots$
751.1.b.d	$751$	$1$	751.b	751.b	$2$	$4$	$4$	$0.375$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-751}) $	None	✓	$2$	$0$	$1$	$0$	$-2$	$0$	$1$		$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{3})q^{5}+\cdots$
775.1.w.b	$775$	$1$	775.w	775.w	$10$	$8$	$2$	$0.387$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$-3$	$0$	$1$	$2$	$1$		$q+(-\zeta_{30}^{5}-\zeta_{30}^{13})q^{2}+(-\zeta_{30}^{3}+\cdots)q^{4}+\cdots$
792.1.bx.a	$792$	$1$	792.bx	792.ax	$30$	$8$	$1$	$0.395$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$1$	$0$	$0$	$1$		$q+\zeta_{30}^{14}q^{2}-\zeta_{30}^{11}q^{3}-\zeta_{30}^{13}q^{4}+\cdots$
792.1.bx.b	$792$	$1$	792.bx	792.ax	$30$	$8$	$1$	$0.395$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$1$	$0$	$0$	$1$		$q+\zeta_{30}^{14}q^{2}+\zeta_{30}^{8}q^{3}-\zeta_{30}^{13}q^{4}+\cdots$
813.1.t.a	$813$	$1$	813.t	813.t	$30$	$8$	$1$	$0.406$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-2$	$0$	$-1$	$1$		$q-\zeta_{30}^{3}q^{3}-\zeta_{30}^{7}q^{4}+(-\zeta_{30}^{7}-\zeta_{30}^{9}+\cdots)q^{7}+\cdots$
815.1.d.e	$815$	$1$	815.d	815.d	$2$	$4$	$4$	$0.407$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-815}) $	None	✓	$2$	$0$	$-1$	$2$	$-4$	$4$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$
815.1.d.f	$815$	$1$	815.d	815.d	$2$	$4$	$4$	$0.407$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-815}) $	None	✓	$2$	$0$	$1$	$-2$	$4$	$-4$	$1$		$q+\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$
836.1.v.a	$836$	$1$	836.v	209.m	$10$	$8$	$2$	$0.417$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$2$	$-3$	$1$		$q+(-\zeta_{30}^{7}-\zeta_{30}^{11})q^{5}+(\zeta_{30}^{4}-\zeta_{30}^{5}+\cdots)q^{7}+\cdots$
837.1.by.a	$837$	$1$	837.by	93.o	$30$	$8$	$1$	$0.418$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-1$	$1$		$q-\zeta_{30}^{9}q^{4}+(\zeta_{30}^{2}+\zeta_{30}^{6})q^{7}+(\zeta_{30}^{2}+\cdots)q^{13}+\cdots$
908.1.d.b	$908$	$1$	908.d	227.b	$2$	$4$	$4$	$0.453$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-227}) $	None	✓	$2$	$0$	$0$	$-2$	$0$	$1$	$1$		$q+\beta _{3}q^{3}+\beta _{1}q^{7}-\beta _{3}q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots$
913.1.h.b	$913$	$1$	913.h	913.h	$10$	$8$	$2$	$0.456$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-83}) $	None		$4$	$0$	$0$	$-3$	$0$	$-3$	$1$		$q+(\zeta_{30}^{2}+\zeta_{30}^{10})q^{3}-\zeta_{30}^{9}q^{4}+(\zeta_{30}^{8}+\cdots)q^{7}+\cdots$
915.1.cn.a	$915$	$1$	915.cn	915.bn	$30$	$8$	$1$	$0.457$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-2$	$2$	$-1$	$0$	$1$		$q+(-\zeta_{30}^{4}+\zeta_{30}^{7})q^{2}+\zeta_{30}^{3}q^{3}+\cdots$
915.1.cn.b	$915$	$1$	915.cn	915.bn	$30$	$8$	$1$	$0.457$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$2$	$-2$	$1$	$0$	$1$		$q+(\zeta_{30}^{4}-\zeta_{30}^{7})q^{2}-\zeta_{30}^{3}q^{3}+(\zeta_{30}^{8}+\cdots)q^{4}+\cdots$
917.1.h.b	$917$	$1$	917.h	917.h	$6$	$8$	$4$	$0.458$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$-1$	$-1$	$1$	$1$		$q+(\zeta_{30}^{8}+\zeta_{30}^{12})q^{3}+\zeta_{30}^{10}q^{4}+\cdots$
943.1.l.b	$943$	$1$	943.l	943.l	$10$	$8$	$2$	$0.471$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$-3$	$2$	$0$	$0$	$1$		$q+(\zeta_{30}^{2}+\zeta_{30}^{10})q^{2}+(-\zeta_{30}^{7}+\zeta_{30}^{8}+\cdots)q^{3}+\cdots$
957.1.p.c	$957$	$1$	957.p	957.p	$10$	$8$	$2$	$0.478$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$-2$	$2$	$0$	$2$	$1$		$q+(\zeta_{30}^{13}-\zeta_{30}^{14})q^{2}+\zeta_{30}^{3}q^{3}+\cdots$
957.1.p.d	$957$	$1$	957.p	957.p	$10$	$8$	$2$	$0.478$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$2$	$-2$	$0$	$2$	$1$		$q+(\zeta_{30}^{4}+\zeta_{30}^{8})q^{2}-\zeta_{30}^{3}q^{3}+(-\zeta_{30}+\cdots)q^{4}+\cdots$
964.1.z.a	$964$	$1$	964.z	964.z	$30$	$8$	$1$	$0.481$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-4$	$0$	$2$	$0$	$1$		$q-\zeta_{30}^{5}q^{2}+\zeta_{30}^{10}q^{4}+(-\zeta_{30}+\zeta_{30}^{8}+\cdots)q^{5}+\cdots$
971.1.b.c	$971$	$1$	971.b	971.b	$2$	$4$	$4$	$0.485$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-971}) $	None	✓	$2$	$0$	$0$	$-2$	$1$	$1$	$1$		$q+\beta _{3}q^{3}+q^{4}+\beta _{1}q^{5}+(-\beta _{2}-\beta _{3})q^{7}+\cdots$
1001.1.y.c	$1001$	$1$	1001.y	1001.y	$6$	$8$	$4$	$0.500$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-143}) $	None		$4$	$0$	$-1$	$-1$	$0$	$1$	$1$		$q+(\zeta_{30}^{4}+\zeta_{30}^{6})q^{2}+(\zeta_{30}^{6}+\zeta_{30}^{14}+\cdots)q^{3}+\cdots$
1001.1.y.d	$1001$	$1$	1001.y	1001.y	$6$	$8$	$4$	$0.500$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-143}) $	None		$4$	$0$	$1$	$-1$	$0$	$-1$	$1$		$q+(-\zeta_{30}^{4}-\zeta_{30}^{6})q^{2}+(\zeta_{30}^{6}+\zeta_{30}^{14}+\cdots)q^{3}+\cdots$
1007.1.d.e	$1007$	$1$	1007.d	1007.d	$2$	$4$	$4$	$0.503$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-1007}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$-2$	$1$		$q-\beta _{1}q^{2}+(\beta _{2}+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$
1007.1.d.f	$1007$	$1$	1007.d	1007.d	$2$	$4$	$4$	$0.503$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-1007}) $	None	✓	$2$	$0$	$1$	$1$	$0$	$-2$	$1$		$q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
1027.1.o.b	$1027$	$1$	1027.o	1027.o	$6$	$8$	$4$	$0.513$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$-1$	$0$	$2$	$0$	$1$		$q+(\zeta_{30}^{4}+\zeta_{30}^{6})q^{2}+(\zeta_{30}^{8}+\zeta_{30}^{10}+\cdots)q^{4}+\cdots$
1057.1.bk.a	$1057$	$1$	1057.bk	1057.ak	$30$	$8$	$1$	$0.528$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-1$	$0$	$0$	$1$	$1$		$q+(-\zeta_{30}-\zeta_{30}^{9})q^{2}+(\zeta_{30}^{2}-\zeta_{30}^{3}+\cdots)q^{4}+\cdots$
1071.1.x.c	$1071$	$1$	1071.x	1071.x	$6$	$8$	$4$	$0.534$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$-1$	$-1$	$1$	$4$	$1$		$q+(-\zeta_{30}-\zeta_{30}^{9})q^{2}+\zeta_{30}q^{3}+(\zeta_{30}^{2}+\cdots)q^{4}+\cdots$
1071.1.x.d	$1071$	$1$	1071.x	1071.x	$6$	$8$	$4$	$0.534$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-119}) $	None		$4$	$0$	$-1$	$1$	$-1$	$-4$	$1$		$q+(-\zeta_{30}^{3}-\zeta_{30}^{7})q^{2}-\zeta_{30}^{7}q^{3}+\cdots$
1100.1.x.a	$1100$	$1$	1100.x	275.v	$10$	$8$	$2$	$0.549$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$-4$	$0$	$1$		$q+(\zeta_{30}^{2}+\zeta_{30}^{4})q^{3}-\zeta_{30}^{5}q^{5}+(\zeta_{30}^{4}+\cdots)q^{9}+\cdots$

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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.