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 56 matches)

Next Download displayed columns to Pari/GP SageMath Magma Oscar

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	11	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
4598.2.a.a	$4598$	$2$	4598.a	1.a	$1$	$1$	$1$	$36.715$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$-4$	$-3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-3q^{7}+\cdots$
4598.2.a.b	$4598$	$2$	4598.a	1.a	$1$	$1$	$1$	$36.715$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$-2$	$3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+3q^{7}+\cdots$
4598.2.a.c	$4598$	$2$	4598.a	1.a	$1$	$1$	$1$	$36.715$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$2$	$3$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+3q^{7}+\cdots$
4598.2.a.d	$4598$	$2$	4598.a	1.a	$1$	$1$	$1$	$36.715$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$-1$	$4$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+4q^{7}-q^{8}-3q^{9}+\cdots$
4598.2.a.e	$4598$	$2$	4598.a	1.a	$1$	$1$	$1$	$36.715$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$0$	$-3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-3q^{7}-q^{8}-3q^{9}-q^{13}+\cdots$
4598.2.a.f	$4598$	$2$	4598.a	1.a	$1$	$1$	$1$	$36.715$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$2$	$-2$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-2q^{7}-q^{8}-3q^{9}+\cdots$
4598.2.a.g	$4598$	$2$	4598.a	1.a	$1$	$1$	$1$	$36.715$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$4$	$-1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{5}-q^{7}-q^{8}-3q^{9}+\cdots$
4598.2.a.h	$4598$	$2$	4598.a	1.a	$1$	$1$	$1$	$36.715$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$0$	$-1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$
4598.2.a.i	$4598$	$2$	4598.a	1.a	$1$	$1$	$1$	$36.715$	$\Q$	None	✓	$1$	$0$	$-1$	$2$	$-2$	$-4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{5}-2q^{6}-4q^{7}+\cdots$
4598.2.a.j	$4598$	$2$	4598.a	1.a	$1$	$1$	$1$	$36.715$	$\Q$	None	✓	$1$	$0$	$-1$	$3$	$-2$	$-1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}-2q^{5}-3q^{6}-q^{7}+\cdots$
4598.2.a.k	$4598$	$2$	4598.a	1.a	$1$	$1$	$1$	$36.715$	$\Q$	None	✓	$1$	$0$	$-1$	$3$	$0$	$0$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}-3q^{6}-q^{8}+6q^{9}+\cdots$
4598.2.a.l	$4598$	$2$	4598.a	1.a	$1$	$1$	$1$	$36.715$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$2$	$-3$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}-3q^{7}+\cdots$
4598.2.a.m	$4598$	$2$	4598.a	1.a	$1$	$1$	$1$	$36.715$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-1$	$-4$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-3q^{9}+\cdots$
4598.2.a.n	$4598$	$2$	4598.a	1.a	$1$	$1$	$1$	$36.715$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{7}+q^{8}-3q^{9}+q^{13}+\cdots$
4598.2.a.o	$4598$	$2$	4598.a	1.a	$1$	$1$	$1$	$36.715$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$4$	$1$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{5}+q^{7}+q^{8}-3q^{9}+\cdots$
4598.2.a.p	$4598$	$2$	4598.a	1.a	$1$	$1$	$1$	$36.715$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$0$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots$
4598.2.a.q	$4598$	$2$	4598.a	1.a	$1$	$1$	$1$	$36.715$	$\Q$	None	✓	$1$	$1$	$1$	$1$	$0$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots$
4598.2.a.r	$4598$	$2$	4598.a	1.a	$1$	$1$	$1$	$36.715$	$\Q$	None	✓	$1$	$0$	$1$	$2$	$-2$	$4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}-2q^{5}+2q^{6}+4q^{7}+\cdots$
4598.2.a.s	$4598$	$2$	4598.a	1.a	$1$	$1$	$1$	$36.715$	$\Q$	None	✓	$1$	$0$	$1$	$3$	$0$	$0$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}+q^{4}+3q^{6}+q^{8}+6q^{9}+\cdots$
4598.2.a.t	$4598$	$2$	4598.a	1.a	$1$	$2$	$2$	$36.715$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$-4$	$1$	$3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+(1-\beta )q^{5}+2q^{6}+\cdots$
4598.2.a.u	$4598$	$2$	4598.a	1.a	$1$	$2$	$2$	$36.715$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$-2$	$-3$	$-1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots$
4598.2.a.v	$4598$	$2$	4598.a	1.a	$1$	$2$	$2$	$36.715$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$-2$	$1$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2\beta q^{3}+q^{4}+(-1+3\beta )q^{5}+\cdots$
4598.2.a.w	$4598$	$2$	4598.a	1.a	$1$	$2$	$2$	$36.715$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$-2$	$-2$	$2$	$4$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots$
4598.2.a.x	$4598$	$2$	4598.a	1.a	$1$	$2$	$2$	$36.715$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$-1$	$-1$	$-1$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta q^{3}+q^{4}-\beta q^{5}+\beta q^{6}+(1+\cdots)q^{7}+\cdots$
4598.2.a.y	$4598$	$2$	4598.a	1.a	$1$	$2$	$2$	$36.715$	$\Q(\sqrt{21}) $	None	✓	$1$	$0$	$-2$	$-1$	$3$	$5$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta q^{3}+q^{4}+(2-\beta )q^{5}+\beta q^{6}+\cdots$
4598.2.a.z	$4598$	$2$	4598.a	1.a	$1$	$2$	$2$	$36.715$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$0$	$-1$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1-3\beta )q^{5}+(1-\beta )q^{7}+\cdots$
4598.2.a.ba	$4598$	$2$	4598.a	1.a	$1$	$2$	$2$	$36.715$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$0$	$-1$	$1$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-2\beta )q^{3}+q^{4}+(-1+\beta )q^{5}+\cdots$
4598.2.a.bb	$4598$	$2$	4598.a	1.a	$1$	$2$	$2$	$36.715$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-4$	$1$	$-3$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2q^{3}+q^{4}+\beta q^{5}-2q^{6}-3\beta q^{7}+\cdots$
4598.2.a.bc	$4598$	$2$	4598.a	1.a	$1$	$2$	$2$	$36.715$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$2$	$-3$	$-1$	$1$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1-\beta )q^{3}+q^{4}+(-1+\beta )q^{5}+\cdots$
4598.2.a.bd	$4598$	$2$	4598.a	1.a	$1$	$2$	$2$	$36.715$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$2$	$-2$	$-3$	$1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots$
4598.2.a.be	$4598$	$2$	4598.a	1.a	$1$	$2$	$2$	$36.715$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-2$	$1$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-2\beta q^{3}+q^{4}+(-1+3\beta )q^{5}+\cdots$
4598.2.a.bf	$4598$	$2$	4598.a	1.a	$1$	$2$	$2$	$36.715$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$-2$	$2$	$-4$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots$
4598.2.a.bg	$4598$	$2$	4598.a	1.a	$1$	$2$	$2$	$36.715$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-1$	$-1$	$1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta q^{3}+q^{4}-\beta q^{5}-\beta q^{6}+(-1+\cdots)q^{7}+\cdots$
4598.2.a.bh	$4598$	$2$	4598.a	1.a	$1$	$2$	$2$	$36.715$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$0$	$-1$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1-3\beta )q^{5}+(-1+\beta )q^{7}+\cdots$
4598.2.a.bi	$4598$	$2$	4598.a	1.a	$1$	$2$	$2$	$36.715$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$0$	$-1$	$-1$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-2\beta )q^{3}+q^{4}+(-1+\beta )q^{5}+\cdots$
4598.2.a.bj	$4598$	$2$	4598.a	1.a	$1$	$2$	$2$	$36.715$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$2$	$1$	$4$	$-3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}+2q^{5}+\beta q^{6}+(-2+\cdots)q^{7}+\cdots$
4598.2.a.bk	$4598$	$2$	4598.a	1.a	$1$	$3$	$3$	$36.715$	3.3.568.1	None	✓	$1$	$1$	$-3$	$-2$	$-1$	$2$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots$
4598.2.a.bl	$4598$	$2$	4598.a	1.a	$1$	$3$	$3$	$36.715$	3.3.404.1	None	✓	$1$	$0$	$-3$	$1$	$4$	$3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{2}q^{3}+q^{4}+(1+2\beta _{1}-\beta _{2})q^{5}+\cdots$
4598.2.a.bm	$4598$	$2$	4598.a	1.a	$1$	$3$	$3$	$36.715$	3.3.469.1	None	✓	$1$	$1$	$-3$	$1$	$5$	$-1$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+(2-\beta _{1})q^{5}-\beta _{1}q^{6}+\cdots$
4598.2.a.bn	$4598$	$2$	4598.a	1.a	$1$	$3$	$3$	$36.715$	3.3.568.1	None	✓	$1$	$1$	$3$	$-2$	$-1$	$-2$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots$
4598.2.a.bo	$4598$	$2$	4598.a	1.a	$1$	$3$	$3$	$36.715$	3.3.621.1	None	✓	$1$	$0$	$3$	$0$	$-3$	$6$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(-1-\beta _{1}-\beta _{2})q^{5}+\cdots$
4598.2.a.bp	$4598$	$2$	4598.a	1.a	$1$	$3$	$3$	$36.715$	3.3.404.1	None	✓	$1$	$0$	$3$	$1$	$4$	$-3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{2}q^{3}+q^{4}+(1+2\beta _{1}-\beta _{2})q^{5}+\cdots$
4598.2.a.bq	$4598$	$2$	4598.a	1.a	$1$	$4$	$4$	$36.715$	4.4.7488.1	None	✓	$1$	$1$	$-4$	$-2$	$-2$	$4$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-\beta _{3})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
4598.2.a.br	$4598$	$2$	4598.a	1.a	$1$	$4$	$4$	$36.715$	4.4.33452.1	None	✓	$1$	$0$	$-4$	$1$	$3$	$1$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+\cdots$
4598.2.a.bs	$4598$	$2$	4598.a	1.a	$1$	$4$	$4$	$36.715$	4.4.258228.1	None	✓	$1$	$0$	$-4$	$2$	$-2$	$-3$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1})q^{3}+q^{4}-\beta _{1}q^{5}+(-1+\cdots)q^{6}+\cdots$
4598.2.a.bt	$4598$	$2$	4598.a	1.a	$1$	$4$	$4$	$36.715$	4.4.7488.1	None	✓	$1$	$1$	$4$	$-2$	$-2$	$-4$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1-\beta _{3})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
4598.2.a.bu	$4598$	$2$	4598.a	1.a	$1$	$4$	$4$	$36.715$	4.4.33452.1	None	✓	$1$	$0$	$4$	$1$	$3$	$-1$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+\cdots$
4598.2.a.bv	$4598$	$2$	4598.a	1.a	$1$	$4$	$4$	$36.715$	4.4.258228.1	None	✓	$1$	$0$	$4$	$2$	$-2$	$3$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{1})q^{3}+q^{4}-\beta _{1}q^{5}+(1+\cdots)q^{6}+\cdots$
4598.2.a.bw	$4598$	$2$	4598.a	1.a	$1$	$8$	$8$	$36.715$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$0$	$-8$	$-2$	$-2$	$14$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{1}q^{3}+q^{4}+(-\beta _{1}-\beta _{3}-\beta _{6}+\cdots)q^{5}+\cdots$
4598.2.a.bx	$4598$	$2$	4598.a	1.a	$1$	$8$	$8$	$36.715$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-8$	$0$	$2$	$-8$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(\beta _{2}+\beta _{4}-\beta _{6})q^{3}+q^{4}-\beta _{3}q^{5}+\cdots$

Next Download displayed columns to Pari/GP SageMath Magma Oscar

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 56 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.