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 58 matches)

Next Download displayed columns for results to

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				A-L signs				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	3	11	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
6864.2.a.a	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	$\Q$	None	✓	$1$	$2$	$0$	$-1$	$-3$	$-5$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}-5q^{7}+q^{9}+q^{11}+q^{13}+\cdots$
6864.2.a.b	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	$\Q$	None	✓	$1$	$2$	$0$	$-1$	$-3$	$-3$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}-3q^{7}+q^{9}+q^{11}-q^{13}+\cdots$
6864.2.a.c	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-2$	$-4$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}-4q^{7}+q^{9}-q^{11}+q^{13}+\cdots$
6864.2.a.d	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-2$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{9}-q^{11}-q^{13}+2q^{15}+\cdots$
6864.2.a.e	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$-2$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{9}+q^{11}+q^{13}+2q^{15}+\cdots$
6864.2.a.f	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-2$	$2$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+2q^{7}+q^{9}-q^{11}+q^{13}+\cdots$
6864.2.a.g	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$-1$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{5}-q^{7}+q^{9}-q^{11}-q^{13}+\cdots$
6864.2.a.h	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$-2$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}+q^{9}+q^{11}+q^{13}+6q^{17}+\cdots$
6864.2.a.i	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$0$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{9}-q^{11}-q^{13}-4q^{17}+\cdots$
6864.2.a.j	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$0$	$4$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{7}+q^{9}+q^{11}+q^{13}+4q^{19}+\cdots$
6864.2.a.k	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$2$	$-4$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}-4q^{7}+q^{9}-q^{11}-q^{13}+\cdots$
6864.2.a.l	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$2$	$-4$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}-4q^{7}+q^{9}-q^{11}-q^{13}+\cdots$
6864.2.a.m	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$2$	$-4$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}-4q^{7}+q^{9}-q^{11}+q^{13}+\cdots$
6864.2.a.n	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$2$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+q^{9}+q^{11}+q^{13}-2q^{15}+\cdots$
6864.2.a.o	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$3$	$1$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}+q^{7}+q^{9}-q^{11}+q^{13}+\cdots$
6864.2.a.p	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$4$	$4$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{5}+4q^{7}+q^{9}-q^{11}-q^{13}+\cdots$
6864.2.a.q	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-3$	$-1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}-q^{7}+q^{9}+q^{11}+q^{13}+\cdots$
6864.2.a.r	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-2$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{9}-q^{11}+q^{13}-2q^{15}+\cdots$
6864.2.a.s	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$-2$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{9}-q^{11}+q^{13}-2q^{15}+\cdots$
6864.2.a.t	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-1$	$-3$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}-3q^{7}+q^{9}-q^{11}+q^{13}+\cdots$
6864.2.a.u	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-1$	$3$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+3q^{7}+q^{9}-q^{11}-q^{13}+\cdots$
6864.2.a.v	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$-4$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{7}+q^{9}+q^{11}-q^{13}+8q^{17}+\cdots$
6864.2.a.w	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$0$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}-q^{11}+q^{13}-4q^{17}+\cdots$
6864.2.a.x	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$0$	$2$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{7}+q^{9}+q^{11}+q^{13}-2q^{17}+\cdots$
6864.2.a.y	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$2$	$-4$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}-4q^{7}+q^{9}+q^{11}-q^{13}+\cdots$
6864.2.a.z	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$2$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}+q^{9}-q^{11}-q^{13}+2q^{15}+\cdots$
6864.2.a.ba	$6864$	$2$	6864.a	1.a	$1$	$1$	$1$	$54.809$	$\Q$	None	✓	$1$	$0$	$0$	$1$	$4$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{5}+q^{9}-q^{11}+q^{13}+4q^{15}+\cdots$
6864.2.a.bb	$6864$	$2$	6864.a	1.a	$1$	$2$	$2$	$54.809$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$-2$	$-4$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-2+\beta )q^{5}+2\beta q^{7}+q^{9}+\cdots$
6864.2.a.bc	$6864$	$2$	6864.a	1.a	$1$	$2$	$2$	$54.809$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$0$	$-2$	$-4$	$4$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-2+\beta )q^{5}+(2+2\beta )q^{7}+q^{9}+\cdots$
6864.2.a.bd	$6864$	$2$	6864.a	1.a	$1$	$2$	$2$	$54.809$	$\Q(\sqrt{41}) $	None	✓	$1$	$1$	$0$	$-2$	$-1$	$-3$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta q^{5}+(-2+\beta )q^{7}+q^{9}+q^{11}+\cdots$
6864.2.a.be	$6864$	$2$	6864.a	1.a	$1$	$2$	$2$	$54.809$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$-2$	$0$	$4$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}+2q^{7}+q^{9}+q^{11}+q^{13}+\cdots$
6864.2.a.bf	$6864$	$2$	6864.a	1.a	$1$	$2$	$2$	$54.809$	$\Q(\sqrt{41}) $	None	✓	$1$	$0$	$0$	$-2$	$4$	$0$	$-$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+q^{9}+q^{11}+q^{13}-2q^{15}+\cdots$
6864.2.a.bg	$6864$	$2$	6864.a	1.a	$1$	$2$	$2$	$54.809$	$\Q(\sqrt{6}) $	None	✓	$1$	$1$	$0$	$2$	$-4$	$4$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-2+\beta )q^{5}+2q^{7}+q^{9}-q^{11}+\cdots$
6864.2.a.bh	$6864$	$2$	6864.a	1.a	$1$	$2$	$2$	$54.809$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$0$	$2$	$-3$	$1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta )q^{5}+(1-\beta )q^{7}+q^{9}+\cdots$
6864.2.a.bi	$6864$	$2$	6864.a	1.a	$1$	$2$	$2$	$54.809$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$2$	$-2$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1+\beta )q^{5}+q^{9}-q^{11}-q^{13}+\cdots$
6864.2.a.bj	$6864$	$2$	6864.a	1.a	$1$	$2$	$2$	$54.809$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$0$	$2$	$-2$	$0$	$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta )q^{5}+q^{9}+q^{11}-q^{13}+\cdots$
6864.2.a.bk	$6864$	$2$	6864.a	1.a	$1$	$2$	$2$	$54.809$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$0$	$2$	$-2$	$4$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1+\beta )q^{5}+2q^{7}+q^{9}+q^{11}+\cdots$
6864.2.a.bl	$6864$	$2$	6864.a	1.a	$1$	$2$	$2$	$54.809$	$\Q(\sqrt{33}) $	None	✓	$1$	$0$	$0$	$2$	$1$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta q^{5}+\beta q^{7}+q^{9}+q^{11}-q^{13}+\cdots$
6864.2.a.bm	$6864$	$2$	6864.a	1.a	$1$	$2$	$2$	$54.809$	$\Q(\sqrt{3}) $	None	✓	$1$	$1$	$0$	$2$	$2$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1+\beta )q^{5}-2\beta q^{7}+q^{9}-q^{11}+\cdots$
6864.2.a.bn	$6864$	$2$	6864.a	1.a	$1$	$3$	$3$	$54.809$	3.3.404.1	None	✓	$1$	$0$	$0$	$-3$	$-4$	$6$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta _{2})q^{5}+(2+\beta _{1}-\beta _{2})q^{7}+\cdots$
6864.2.a.bo	$6864$	$2$	6864.a	1.a	$1$	$3$	$3$	$54.809$	3.3.892.1	None	✓	$1$	$1$	$0$	$-3$	$-1$	$-5$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{1}q^{5}+(-2+\beta _{1}-\beta _{2})q^{7}+\cdots$
6864.2.a.bp	$6864$	$2$	6864.a	1.a	$1$	$3$	$3$	$54.809$	3.3.148.1	None	✓	$1$	$1$	$0$	$-3$	$0$	$2$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{2}q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots$
6864.2.a.bq	$6864$	$2$	6864.a	1.a	$1$	$3$	$3$	$54.809$	3.3.148.1	None	✓	$1$	$0$	$0$	$-3$	$0$	$2$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{2}q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots$
6864.2.a.br	$6864$	$2$	6864.a	1.a	$1$	$3$	$3$	$54.809$	3.3.564.1	None	✓	$1$	$0$	$0$	$-3$	$2$	$-4$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1-\beta _{1})q^{5}+(-1+\beta _{2})q^{7}+\cdots$
6864.2.a.bs	$6864$	$2$	6864.a	1.a	$1$	$3$	$3$	$54.809$	3.3.148.1	None	✓	$1$	$1$	$0$	$-3$	$4$	$2$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta _{1})q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+\cdots$
6864.2.a.bt	$6864$	$2$	6864.a	1.a	$1$	$3$	$3$	$54.809$	3.3.404.1	None	✓	$1$	$0$	$0$	$-3$	$4$	$4$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1+2\beta _{1}-\beta _{2})q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots$
6864.2.a.bu	$6864$	$2$	6864.a	1.a	$1$	$3$	$3$	$54.809$	3.3.564.1	None	✓	$1$	$1$	$0$	$3$	$-2$	$-2$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-\beta _{1}+\beta _{2})q^{5}+(-1-\beta _{2})q^{7}+\cdots$
6864.2.a.bv	$6864$	$2$	6864.a	1.a	$1$	$3$	$3$	$54.809$	3.3.1620.1	None	✓	$1$	$0$	$0$	$3$	$0$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{1}q^{5}-\beta _{2}q^{7}+q^{9}+q^{11}+\cdots$
6864.2.a.bw	$6864$	$2$	6864.a	1.a	$1$	$4$	$4$	$54.809$	4.4.70164.1	None	✓	$1$	$1$	$0$	$-4$	$1$	$-1$	$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+(1+\beta _{2}-\beta _{3})q^{5}+\beta _{2}q^{7}+q^{9}+\cdots$
6864.2.a.bx	$6864$	$2$	6864.a	1.a	$1$	$4$	$4$	$54.809$	4.4.83476.1	None	✓	$1$	$0$	$0$	$-4$	$2$	$2$	$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{3}q^{5}+(1-\beta _{1}-\beta _{3})q^{7}+q^{9}+\cdots$

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 58 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.