LMFDB - Newform search results

Refine search

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
		Only for weight 1:

				Sort order	Select

Results (1-50 of 6114 matches)

Next Download displayed columns for results to

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
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		$4$	$0$	$1$	$-1$	$0$	$-1$	$1$		$q+(-\zeta_{30}^{4}-\zeta_{30}^{6})q^{2}+(\zeta_{30}^{6}+\zeta_{30}^{14}+\cdots)q^{3}+\cdots$
1003.1.h.b	$1003$	$1$	1003.h	1003.h	$8$	$8$	$2$	$0.501$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$2$		$q+(-\zeta_{24}-\zeta_{24}^{2})q^{3}-\zeta_{24}^{6}q^{4}+(\zeta_{24}^{5}+\cdots)q^{5}+\cdots$
1004.1.d.b	$1004$	$1$	1004.d	251.b	$2$	$6$	$6$	$0.501$	$\Q(\zeta_{21})^+$	$D_{21}$	$\Q(\sqrt{-251}) $	None	✓	$2$	$0$	$0$	$-2$	$1$	$1$	$1$		$q+(-1-\beta _{3}+\beta _{5})q^{3}+\beta _{4}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots$
1008.1.dt.a	$1008$	$1$	1008.dt	112.u	$12$	$8$	$2$	$0.503$	$\Q(\zeta_{24})$	$S_{4}$	None	None		$8$	$0$	$0$	$0$	$0$	$-4$	$1$		$q-\zeta_{24}^{11}q^{2}-\zeta_{24}^{10}q^{4}+\zeta_{24}^{11}q^{5}+\cdots$
1008.1.ed.a	$1008$	$1$	1008.ed	336.at	$12$	$8$	$2$	$0.503$	$\Q(\zeta_{24})$	$S_{4}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}q^{5}+\zeta_{24}^{2}q^{7}+\cdots$
1011.1.q.a	$1011$	$1$	1011.q	1011.q	$14$	$6$	$1$	$0.505$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-2$	$1$		$q-\zeta_{14}^{6}q^{3}+\zeta_{14}^{6}q^{4}+(-\zeta_{14}-\zeta_{14}^{5}+\cdots)q^{7}+\cdots$
1011.1.r.a	$1011$	$1$	1011.r	1011.r	$14$	$6$	$1$	$0.505$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{14}^{3}q^{3}-\zeta_{14}^{3}q^{4}+(\zeta_{14}^{4}+\zeta_{14}^{6}+\cdots)q^{7}+\cdots$
1015.1.br.a	$1015$	$1$	1015.br	1015.ar	$14$	$6$	$1$	$0.507$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$0$	$-1$	$-1$	$1$		$q+(-\zeta_{14}^{2}+\zeta_{14}^{4})q^{3}-\zeta_{14}^{4}q^{4}+\cdots$
1015.1.br.b	$1015$	$1$	1015.br	1015.ar	$14$	$6$	$1$	$0.507$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$0$	$1$	$1$	$1$		$q+(\zeta_{14}^{2}-\zeta_{14}^{4})q^{3}-\zeta_{14}^{4}q^{4}-\zeta_{14}^{2}q^{5}+\cdots$
1015.1.bs.a	$1015$	$1$	1015.bs	1015.as	$14$	$6$	$1$	$0.507$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$-2$	$-1$	$-1$	$1$		$q+(-\zeta_{14}^{3}+\zeta_{14}^{6})q^{3}+\zeta_{14}^{6}q^{4}+\cdots$
1015.1.bs.b	$1015$	$1$	1015.bs	1015.as	$14$	$6$	$1$	$0.507$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$2$	$1$	$1$	$1$		$q+(\zeta_{14}^{3}-\zeta_{14}^{6})q^{3}+\zeta_{14}^{6}q^{4}+\zeta_{14}^{3}q^{5}+\cdots$
1019.1.b.a	$1019$	$1$	1019.b	1019.b	$2$	$6$	$6$	$0.509$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-1019}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$0$	$1$		$q-\beta _{3}q^{3}+q^{4}+\beta _{2}q^{5}+(\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{9}+\cdots$
1023.1.dk.a	$1023$	$1$	1023.dk	1023.ck	$30$	$8$	$1$	$0.511$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-1$	$-3$	$0$	$1$		$q-\zeta_{30}^{14}q^{3}+\zeta_{30}^{3}q^{4}+(-\zeta_{30}^{9}+\cdots)q^{5}+\cdots$
1023.1.dk.b	$1023$	$1$	1023.dk	1023.ck	$30$	$8$	$1$	$0.511$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$1$	$3$	$0$	$1$		$q+\zeta_{30}^{8}q^{3}+\zeta_{30}^{3}q^{4}+(\zeta_{30}^{9}-\zeta_{30}^{11}+\cdots)q^{5}+\cdots$
1027.1.o.b	$1027$	$1$	1027.o	1027.o	$6$	$8$	$4$	$0.513$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$-1$	$0$	$2$	$0$	$1$		$q+(\zeta_{30}^{4}+\zeta_{30}^{6})q^{2}+(\zeta_{30}^{8}+\zeta_{30}^{10}+\cdots)q^{4}+\cdots$
1027.1.s.b	$1027$	$1$	1027.s	1027.s	$6$	$8$	$4$	$0.513$	$\Q(\zeta_{15})$	$D_{30}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q+(-\zeta_{30}^{8}+\zeta_{30}^{12})q^{2}+(-\zeta_{30}+\zeta_{30}^{5}+\cdots)q^{4}+\cdots$
1028.1.j.a	$1028$	$1$	1028.j	1028.j	$16$	$8$	$1$	$0.513$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-8$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}+(\zeta_{16}^{6}+\zeta_{16}^{7})q^{5}-q^{8}+\cdots$
1029.1.l.a	$1029$	$1$	1029.l	147.l	$14$	$6$	$1$	$0.514$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q-\zeta_{14}^{2}q^{3}+\zeta_{14}^{6}q^{4}+\zeta_{14}^{4}q^{9}+\cdots$
1032.1.bv.a	$1032$	$1$	1032.bv	1032.av	$14$	$6$	$1$	$0.515$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q-\zeta_{14}^{5}q^{2}+\zeta_{14}^{5}q^{3}-\zeta_{14}^{3}q^{4}+\cdots$
1032.1.bv.b	$1032$	$1$	1032.bv	1032.av	$14$	$6$	$1$	$0.515$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+\zeta_{14}^{5}q^{2}+\zeta_{14}^{6}q^{3}-\zeta_{14}^{3}q^{4}+\cdots$
1035.1.bd.a	$1035$	$1$	1035.bd	115.i	$22$	$10$	$1$	$0.517$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+(\zeta_{22}^{2}-\zeta_{22}^{10})q^{2}+(\zeta_{22}+\zeta_{22}^{4}+\cdots)q^{4}+\cdots$
1035.1.bd.b	$1035$	$1$	1035.bd	115.i	$22$	$10$	$1$	$0.517$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+(-\zeta_{22}^{2}+\zeta_{22}^{10})q^{2}+(\zeta_{22}+\zeta_{22}^{4}+\cdots)q^{4}+\cdots$
1044.1.o.a	$1044$	$1$	1044.o	1044.o	$6$	$6$	$3$	$0.521$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{6}q^{2}+\zeta_{18}^{4}q^{3}-\zeta_{18}^{3}q^{4}+\cdots$
1044.1.o.b	$1044$	$1$	1044.o	1044.o	$6$	$6$	$3$	$0.521$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-29}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{6}q^{2}+\zeta_{18}^{7}q^{3}-\zeta_{18}^{3}q^{4}+\cdots$
1044.1.bb.a	$1044$	$1$	1044.bb	116.j	$14$	$6$	$1$	$0.521$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$2$	$0$	$1$		$q+\zeta_{14}q^{2}+\zeta_{14}^{2}q^{4}+(-\zeta_{14}^{4}+\zeta_{14}^{5}+\cdots)q^{5}+\cdots$
1045.1.w.e	$1045$	$1$	1045.w	1045.w	$10$	$8$	$2$	$0.522$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$-2$	$0$	$5$		$q+(-\zeta_{20}^{3}-\zeta_{20}^{9})q^{2}+(\zeta_{20}^{7}+\zeta_{20}^{9}+\cdots)q^{3}+\cdots$
1045.1.br.a	$1045$	$1$	1045.br	1045.ar	$20$	$8$	$1$	$0.522$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$-8$	$1$		$q-\zeta_{20}^{3}q^{4}+\zeta_{20}^{4}q^{5}+(-1-\zeta_{20}+\cdots)q^{7}+\cdots$
1045.1.br.b	$1045$	$1$	1045.br	1045.ar	$20$	$8$	$1$	$0.522$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$-2$	$1$		$q-\zeta_{20}^{3}q^{4}+\zeta_{20}^{8}q^{5}+(\zeta_{20}^{5}-\zeta_{20}^{6}+\cdots)q^{7}+\cdots$
1048.1.k.b	$1048$	$1$	1048.k	1048.k	$10$	$8$	$2$	$0.523$	$\Q(\zeta_{20})$	$A_{5}$	None	None		$4$	$0$	$0$	$-4$	$0$	$0$	$1$		$q+\zeta_{20}^{9}q^{2}+(-\zeta_{20}^{2}+\zeta_{20}^{4})q^{3}+\cdots$
1055.1.d.h	$1055$	$1$	1055.d	1055.d	$2$	$6$	$6$	$0.527$	$\Q(\zeta_{36})^+$	$D_{18}$	$\Q(\sqrt{-1055}) $	None	✓	$4$	$0$	$0$	$0$	$-6$	$0$	$1$		$q+\beta _{3}q^{2}-\beta _{1}q^{3}+2q^{4}-q^{5}+(-2\beta _{2}+\cdots)q^{6}+\cdots$
1057.1.bk.a	$1057$	$1$	1057.bk	1057.ak	$30$	$8$	$1$	$0.528$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-1$	$0$	$0$	$1$	$1$		$q+(-\zeta_{30}-\zeta_{30}^{9})q^{2}+(\zeta_{30}^{2}-\zeta_{30}^{3}+\cdots)q^{4}+\cdots$
1063.1.b.a	$1063$	$1$	1063.b	1063.b	$2$	$9$	$9$	$0.531$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-1063}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots$
1064.1.br.a	$1064$	$1$	1064.br	1064.ar	$6$	$6$	$3$	$0.531$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{6}q^{2}+(-\zeta_{18}-\zeta_{18}^{5})q^{3}-\zeta_{18}^{3}q^{4}+\cdots$
1064.1.br.b	$1064$	$1$	1064.br	1064.ar	$6$	$6$	$3$	$0.531$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-38}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{6}q^{2}+(-\zeta_{18}^{2}-\zeta_{18}^{4})q^{3}+\cdots$
1064.1.br.c	$1064$	$1$	1064.br	1064.ar	$6$	$8$	$4$	$0.531$	$\Q(\zeta_{24})$	$S_{4}$	None	None		$8$	$0$	$0$	$0$	$0$	$-4$	$1$		$q-\zeta_{24}^{5}q^{2}+(-\zeta_{24}-\zeta_{24}^{7})q^{3}+\zeta_{24}^{10}q^{4}+\cdots$
1064.1.ef.a	$1064$	$1$	1064.ef	1064.df	$18$	$6$	$1$	$0.531$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-14}) $	None		$4$	$0$	$0$	$0$	$-3$	$-3$	$1$		$q-\zeta_{18}^{5}q^{2}-\zeta_{18}^{2}q^{3}-\zeta_{18}q^{4}+(-\zeta_{18}^{3}+\cdots)q^{5}+\cdots$
1064.1.ef.b	$1064$	$1$	1064.ef	1064.df	$18$	$6$	$1$	$0.531$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-14}) $	None		$4$	$0$	$0$	$0$	$3$	$-3$	$1$		$q-\zeta_{18}^{5}q^{2}+\zeta_{18}^{2}q^{3}-\zeta_{18}q^{4}+(\zeta_{18}^{3}+\cdots)q^{5}+\cdots$
1067.1.u.a	$1067$	$1$	1067.u	1067.u	$16$	$8$	$1$	$0.533$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{16}-\zeta_{16}^{5})q^{3}-\zeta_{16}^{2}q^{4}+(\zeta_{16}^{6}+\cdots)q^{5}+\cdots$
1067.1.y.a	$1067$	$1$	1067.y	1067.y	$24$	$8$	$1$	$0.533$	$\Q(\zeta_{24})$	$D_{24}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{24}^{3}+\zeta_{24}^{11})q^{3}-\zeta_{24}^{2}q^{4}+\cdots$
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		$4$	$0$	$-1$	$1$	$-1$	$-4$	$1$		$q+(-\zeta_{30}^{3}-\zeta_{30}^{7})q^{2}-\zeta_{30}^{7}q^{3}+\cdots$
1071.1.ci.a	$1071$	$1$	1071.ci	1071.bi	$12$	$8$	$2$	$0.534$	$\Q(\zeta_{24})$	$S_{4}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{24}^{10}q^{2}-\zeta_{24}^{5}q^{3}+\zeta_{24}^{5}q^{5}+\cdots$
1075.1.c.c	$1075$	$1$	1075.c	43.b	$2$	$6$	$6$	$0.536$	6.0.153664.1	$D_{7}$	$\Q(\sqrt{-215}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{3}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots$
1079.1.d.a	$1079$	$1$	1079.d	1079.d	$2$	$8$	$8$	$0.538$	$\Q(\zeta_{34})^+$	$D_{17}$	$\Q(\sqrt{-1079}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$0$	$1$		$q+\beta _{6}q^{2}-\beta _{1}q^{3}+(1-\beta _{5})q^{4}-\beta _{3}q^{5}+\cdots$
1079.1.d.b	$1079$	$1$	1079.d	1079.d	$2$	$8$	$8$	$0.538$	$\Q(\zeta_{34})^+$	$D_{17}$	$\Q(\sqrt{-1079}) $	None	✓	$2$	$0$	$1$	$-1$	$1$	$0$	$1$		$q-\beta _{2}q^{2}+\beta _{6}q^{3}+(1+\beta _{4})q^{4}+\beta _{1}q^{5}+\cdots$
1080.1.u.a	$1080$	$1$	1080.u	40.i	$4$	$8$	$4$	$0.539$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$4$	$1$		$q+\zeta_{24}^{3}q^{2}+\zeta_{24}^{6}q^{4}-\zeta_{24}q^{5}+(-\zeta_{24}^{2}+\cdots)q^{7}+\cdots$
1083.1.l.a	$1083$	$1$	1083.l	57.l	$18$	$6$	$1$	$0.540$	$\Q(\zeta_{18})$	$D_{3}$	$\Q(\sqrt{-3}) $	None		$12$	$0$	$0$	$0$	$0$	$3$	$1$		$q+\zeta_{18}^{8}q^{3}+\zeta_{18}^{4}q^{4}+\zeta_{18}^{3}q^{7}+\cdots$
1083.1.l.b	$1083$	$1$	1083.l	57.l	$18$	$6$	$1$	$0.540$	$\Q(\zeta_{18})$	$D_{3}$	$\Q(\sqrt{-3}) $	None		$12$	$0$	$0$	$0$	$0$	$3$	$1$		$q-\zeta_{18}^{8}q^{3}+\zeta_{18}^{4}q^{4}+\zeta_{18}^{3}q^{7}+\cdots$
1085.1.bh.a	$1085$	$1$	1085.bh	1085.ah	$6$	$6$	$3$	$0.541$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}+\zeta_{18}^{2})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{3}+\cdots)q^{4}+\cdots$

Next Download displayed columns for results to

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 6114 matches)

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.