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 149 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
87.1.d.a	$87$	$1$	87.d	87.d	$2$	$1$	$1$	$0.043$	$\Q$	$D_{3}$	$\Q(\sqrt{-87}) $	None	✓	$2$	$0$	$-1$	$1$	$0$	$-1$	$1$		$q-q^{2}+q^{3}-q^{6}-q^{7}+q^{8}+q^{9}+\cdots$
87.1.d.b	$87$	$1$	87.d	87.d	$2$	$1$	$1$	$0.043$	$\Q$	$D_{3}$	$\Q(\sqrt{-87}) $	None	✓	$2$	$0$	$1$	$-1$	$0$	$-1$	$1$		$q+q^{2}-q^{3}-q^{6}-q^{7}-q^{8}+q^{9}+\cdots$
609.1.p.a	$609$	$1$	609.p	609.p	$6$	$6$	$3$	$0.304$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$0$	$-3$	$0$	$0$	$1$		$q+(-\zeta_{18}-\zeta_{18}^{5})q^{2}+\zeta_{18}^{6}q^{3}+(-\zeta_{18}+\cdots)q^{4}+\cdots$
609.1.p.b	$609$	$1$	609.p	609.p	$6$	$6$	$3$	$0.304$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$0$	$3$	$0$	$0$	$1$		$q+(-\zeta_{18}^{2}-\zeta_{18}^{4})q^{2}-\zeta_{18}^{6}q^{3}+\cdots$
696.1.n.e	$696$	$1$	696.n	696.n	$2$	$2$	$2$	$0.347$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-6}) $, $\Q(\sqrt{-87}) $	$\Q(\sqrt{58}) $		$8$	$0$	$0$	$0$	$0$	$-4$	$1$		$q-iq^{2}+iq^{3}-q^{4}+q^{6}-q^{7}+iq^{8}+\cdots$
696.1.n.f	$696$	$1$	696.n	696.n	$2$	$4$	$4$	$0.347$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-87}) $	None		$8$	$0$	$0$	$0$	$0$	$4$	$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{4}q^{6}+\cdots$
783.1.d.a	$783$	$1$	783.d	87.d	$2$	$3$	$3$	$0.391$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-87}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{1}q^{7}+(-1+\cdots)q^{8}+\cdots$
783.1.d.b	$783$	$1$	783.d	87.d	$2$	$3$	$3$	$0.391$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-87}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{1}q^{7}+(1+\beta _{1}+\cdots)q^{8}+\cdots$
957.1.p.a	$957$	$1$	957.p	957.p	$10$	$4$	$1$	$0.478$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$-2$	$-1$	$0$	$-2$	$1$		$q+(-\zeta_{10}-\zeta_{10}^{3})q^{2}-\zeta_{10}q^{3}+(-\zeta_{10}+\cdots)q^{4}+\cdots$
957.1.p.b	$957$	$1$	957.p	957.p	$10$	$4$	$1$	$0.478$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$2$	$1$	$0$	$-2$	$1$		$q+(\zeta_{10}+\zeta_{10}^{3})q^{2}+\zeta_{10}q^{3}+(-\zeta_{10}+\cdots)q^{4}+\cdots$
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		$4$	$0$	$2$	$-2$	$0$	$2$	$1$		$q+(\zeta_{30}^{4}+\zeta_{30}^{8})q^{2}-\zeta_{30}^{3}q^{3}+(-\zeta_{30}+\cdots)q^{4}+\cdots$
1044.1.g.c	$1044$	$1$	1044.g	116.d	$2$	$2$	$2$	$0.521$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-87}) $	$\Q(\sqrt{87}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-q^{4}+iq^{8}+q^{13}+q^{16}+\cdots$
1044.1.g.d	$1044$	$1$	1044.g	116.d	$2$	$4$	$4$	$0.521$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-87}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-\zeta_{12}^{2}-\zeta_{12}^{4}+\cdots)q^{7}+\cdots$
1131.1.d.a	$1131$	$1$	1131.d	1131.d	$2$	$1$	$1$	$0.564$	$\Q$	$D_{2}$	$\Q(\sqrt{-87}) $, $\Q(\sqrt{-1131}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}+q^{4}+q^{9}-q^{12}-q^{13}+q^{16}+\cdots$
1131.1.d.b	$1131$	$1$	1131.d	1131.d	$2$	$1$	$1$	$0.564$	$\Q$	$D_{2}$	$\Q(\sqrt{-87}) $, $\Q(\sqrt{-1131}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots$
1131.1.d.c	$1131$	$1$	1131.d	1131.d	$2$	$2$	$2$	$0.564$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{2}-q^{3}+(-1-\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{4}+\cdots$
1131.1.d.d	$1131$	$1$	1131.d	1131.d	$2$	$2$	$2$	$0.564$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+(-\zeta_{6}-\zeta_{6}^{2})q^{2}+q^{3}+(-1-\zeta_{6}+\cdots)q^{4}+\cdots$
1131.1.v.a	$1131$	$1$	1131.v	1131.v	$6$	$2$	$1$	$0.564$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$-2$	$-1$	$0$	$1$	$1$		$q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-3\zeta_{6}q^{4}-2\zeta_{6}q^{6}+\cdots$
1131.1.v.b	$1131$	$1$	1131.v	1131.v	$6$	$2$	$1$	$0.564$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$-1$	$1$	$0$	$-2$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}+\zeta_{6}q^{6}-\zeta_{6}q^{7}+\cdots$
1131.1.v.c	$1131$	$1$	1131.v	1131.v	$6$	$2$	$1$	$0.564$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$-1$	$1$	$0$	$1$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}+\zeta_{6}q^{6}+\zeta_{6}q^{7}+\cdots$
1131.1.v.d	$1131$	$1$	1131.v	1131.v	$6$	$2$	$1$	$0.564$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$1$	$-1$	$0$	$-2$	$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{6}-\zeta_{6}q^{7}+\cdots$
1131.1.v.e	$1131$	$1$	1131.v	1131.v	$6$	$2$	$1$	$0.564$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$1$	$-1$	$0$	$1$	$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{6}+\zeta_{6}q^{7}+\cdots$
1131.1.v.f	$1131$	$1$	1131.v	1131.v	$6$	$2$	$1$	$0.564$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$2$	$1$	$0$	$1$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-3\zeta_{6}q^{4}-2\zeta_{6}q^{6}+\cdots$
1131.1.bb.a	$1131$	$1$	1131.bb	1131.ab	$6$	$2$	$1$	$0.564$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$-3$	$-1$	$0$	$0$	$1$		$q+(-1-\zeta_{6})q^{2}+\zeta_{6}^{2}q^{3}+(1+\zeta_{6}+\cdots)q^{4}+\cdots$
1131.1.bb.b	$1131$	$1$	1131.bb	1131.ab	$6$	$2$	$1$	$0.564$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$-3$	$1$	$0$	$-3$	$1$		$q+(-1-\zeta_{6})q^{2}-\zeta_{6}^{2}q^{3}+(1+\zeta_{6}+\cdots)q^{4}+\cdots$
1131.1.bb.c	$1131$	$1$	1131.bb	1131.ab	$6$	$2$	$1$	$0.564$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$0$	$-1$	$0$	$3$	$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+(1-\zeta_{6}^{2})q^{7}-\zeta_{6}q^{9}+\cdots$
1131.1.bb.d	$1131$	$1$	1131.bb	1131.ab	$6$	$2$	$1$	$0.564$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$0$	$1$	$0$	$3$	$1$		$q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+(1-\zeta_{6}^{2})q^{7}-\zeta_{6}q^{9}+\cdots$
1131.1.bb.e	$1131$	$1$	1131.bb	1131.ab	$6$	$2$	$1$	$0.564$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$3$	$-1$	$0$	$-3$	$1$		$q+(1+\zeta_{6})q^{2}+\zeta_{6}^{2}q^{3}+(1+\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{4}+\cdots$
1131.1.bb.f	$1131$	$1$	1131.bb	1131.ab	$6$	$2$	$1$	$0.564$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$3$	$1$	$0$	$0$	$1$		$q+(1+\zeta_{6})q^{2}-\zeta_{6}^{2}q^{3}+(1+\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{4}+\cdots$
1392.1.i.a	$1392$	$1$	1392.i	87.d	$2$	$1$	$1$	$0.695$	$\Q$	$D_{3}$	$\Q(\sqrt{-87}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$1$	$1$		$q-q^{3}+q^{7}+q^{9}+q^{11}-q^{13}-q^{17}+\cdots$
1392.1.i.b	$1392$	$1$	1392.i	87.d	$2$	$1$	$1$	$0.695$	$\Q$	$D_{3}$	$\Q(\sqrt{-87}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$1$	$1$		$q+q^{3}+q^{7}+q^{9}-q^{11}-q^{13}+q^{17}+\cdots$
1392.1.z.a	$1392$	$1$	1392.z	1392.z	$4$	$4$	$2$	$0.695$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-87}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{3}q^{2}+\zeta_{8}q^{3}-\zeta_{8}^{2}q^{4}+q^{6}+\cdots$
1392.1.z.b	$1392$	$1$	1392.z	1392.z	$4$	$8$	$4$	$0.695$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-87}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{9}q^{3}-\zeta_{24}^{2}q^{4}+\cdots$
1479.1.h.a	$1479$	$1$	1479.h	1479.h	$2$	$2$	$2$	$0.738$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-51}) $, $\Q(\sqrt{-87}) $	$\Q(\sqrt{493}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}-q^{4}-q^{9}+iq^{11}+iq^{12}+\cdots$
1479.1.h.f	$1479$	$1$	1479.h	1479.h	$2$	$4$	$4$	$0.738$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-87}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{12}+\zeta_{12}^{5})q^{2}-\zeta_{12}^{3}q^{3}+(1+\cdots)q^{4}+\cdots$
1479.1.j.a	$1479$	$1$	1479.j	1479.j	$4$	$4$	$2$	$0.738$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-87}) $	None		$8$	$0$	$0$	$0$	$0$	$-4$	$1$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}-\zeta_{8}q^{3}-q^{4}+(-1+\cdots)q^{6}+\cdots$
1479.1.j.b	$1479$	$1$	1479.j	1479.j	$4$	$8$	$4$	$0.738$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-87}) $	None		$8$	$0$	$0$	$0$	$0$	$4$	$1$		$q+(-\zeta_{24}^{5}-\zeta_{24}^{7})q^{2}+\zeta_{24}^{9}q^{3}+\cdots$
1479.1.x.a	$1479$	$1$	1479.x	1479.x	$8$	$8$	$2$	$0.738$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-87}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{16}-\zeta_{16}^{3})q^{2}-\zeta_{16}q^{3}+(\zeta_{16}^{2}+\cdots)q^{4}+\cdots$
1479.1.x.b	$1479$	$1$	1479.x	1479.x	$8$	$16$	$4$	$0.738$	$\Q(\zeta_{48})$	$D_{24}$	$\Q(\sqrt{-87}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{48}^{17}-\zeta_{48}^{19})q^{2}+\zeta_{48}^{3}q^{3}+\cdots$
1827.1.b.b	$1827$	$1$	1827.b	203.c	$2$	$2$	$2$	$0.912$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-87}) $	$\Q(\sqrt{609}) $		$8$	$0$	$0$	$0$	$0$	$2$	$1$		$q-iq^{2}-3q^{4}+q^{7}+4iq^{8}+iq^{11}+\cdots$
1827.1.b.c	$1827$	$1$	1827.b	203.c	$2$	$4$	$4$	$0.912$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-87}) $	None		$8$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-\zeta_{12}^{3}q^{2}+\zeta_{12}^{4}q^{7}-\zeta_{12}^{3}q^{8}+\cdots$
1827.1.bj.a	$1827$	$1$	1827.bj	203.i	$6$	$12$	$6$	$0.912$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-87}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{36}^{11}+\zeta_{36}^{13})q^{2}+(-\zeta_{36}^{4}+\cdots)q^{4}+\cdots$
2088.1.b.a	$2088$	$1$	2088.b	232.b	$2$	$1$	$1$	$1.042$	$\Q$	$D_{2}$	$\Q(\sqrt{-87}) $, $\Q(\sqrt{-58}) $	$\Q(\sqrt{6}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}+q^{16}+q^{25}+q^{29}+\cdots$
2088.1.b.b	$2088$	$1$	2088.b	232.b	$2$	$1$	$1$	$1.042$	$\Q$	$D_{2}$	$\Q(\sqrt{-87}) $, $\Q(\sqrt{-58}) $	$\Q(\sqrt{6}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}+q^{16}+q^{25}-q^{29}+\cdots$
2088.1.b.c	$2088$	$1$	2088.b	232.b	$2$	$2$	$2$	$1.042$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{7}+\cdots$
2088.1.b.d	$2088$	$1$	2088.b	232.b	$2$	$2$	$2$	$1.042$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{7}+\cdots$
2175.1.b.a	$2175$	$1$	2175.b	435.b	$2$	$2$	$2$	$1.085$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-iq^{3}-q^{6}-iq^{7}-iq^{8}+\cdots$
2175.1.b.b	$2175$	$1$	2175.b	435.b	$2$	$2$	$2$	$1.085$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-iq^{3}-q^{6}+iq^{7}-iq^{8}+\cdots$
2175.1.b.c	$2175$	$1$	2175.b	435.b	$2$	$6$	$6$	$1.085$	6.0.419904.1	$D_{9}$	$\Q(\sqrt{-87}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\beta _{5}q^{2}-\beta _{3}q^{3}+(-1-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots$

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 149 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.