LMFDB - Newform search results

Refine search

Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

				Sort order	Select

Results (1-50 of 70 matches)

Next Download displayed columns for results to

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	3	11	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
9801.2.a.a	$9801$	$2$	9801.a	1.a	$1$	$1$	$1$	$78.261$	$\Q$	None	✓				99.2.e.c	$1$	$1$	$-2$	$0$	$2$	$-4$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}+2q^{5}-4q^{7}-4q^{10}+\cdots$
9801.2.a.b	$9801$	$2$	9801.a	1.a	$1$	$1$	$1$	$78.261$	$\Q$	None	✓	✓			9801.2.a.b	$1$	$0$	$-1$	$0$	$-2$	$2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-2q^{5}+2q^{7}+3q^{8}+2q^{10}+\cdots$
9801.2.a.c	$9801$	$2$	9801.a	1.a	$1$	$1$	$1$	$78.261$	$\Q$	None	✓				99.2.e.a	$1$	$0$	$-1$	$0$	$1$	$-4$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{5}-4q^{7}+3q^{8}-q^{10}+\cdots$
9801.2.a.d	$9801$	$2$	9801.a	1.a	$1$	$1$	$1$	$78.261$	$\Q$	None	✓				891.2.a.b	$1$	$0$	$-1$	$0$	$1$	$2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{5}+2q^{7}+3q^{8}-q^{10}+\cdots$
9801.2.a.e	$9801$	$2$	9801.a	1.a	$1$	$1$	$1$	$78.261$	$\Q$	None	✓	✓			9801.2.a.b	$1$	$0$	$-1$	$0$	$2$	$-2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+2q^{5}-2q^{7}+3q^{8}-2q^{10}+\cdots$
9801.2.a.f	$9801$	$2$	9801.a	1.a	$1$	$1$	$1$	$78.261$	$\Q$	None	✓				99.2.e.b	$1$	$0$	$0$	$0$	$-3$	$4$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-3q^{5}+4q^{7}-2q^{13}+4q^{16}+\cdots$
9801.2.a.g	$9801$	$2$	9801.a	1.a	$1$	$1$	$1$	$78.261$	$\Q$	None	✓				99.2.e.b	$1$	$1$	$0$	$0$	$3$	$4$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+3q^{5}+4q^{7}-2q^{13}+4q^{16}+\cdots$
9801.2.a.h	$9801$	$2$	9801.a	1.a	$1$	$1$	$1$	$78.261$	$\Q$	None	✓	✓			9801.2.a.b	$1$	$0$	$1$	$0$	$-2$	$-2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-2q^{5}-2q^{7}-3q^{8}-2q^{10}+\cdots$
9801.2.a.i	$9801$	$2$	9801.a	1.a	$1$	$1$	$1$	$78.261$	$\Q$	None	✓				99.2.e.a	$1$	$1$	$1$	$0$	$-1$	$-4$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{5}-4q^{7}-3q^{8}-q^{10}+\cdots$
9801.2.a.j	$9801$	$2$	9801.a	1.a	$1$	$1$	$1$	$78.261$	$\Q$	None	✓				891.2.a.b	$1$	$0$	$1$	$0$	$-1$	$2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{5}+2q^{7}-3q^{8}-q^{10}+\cdots$
9801.2.a.k	$9801$	$2$	9801.a	1.a	$1$	$1$	$1$	$78.261$	$\Q$	None	✓	✓			9801.2.a.b	$1$	$0$	$1$	$0$	$2$	$2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+2q^{5}+2q^{7}-3q^{8}+2q^{10}+\cdots$
9801.2.a.l	$9801$	$2$	9801.a	1.a	$1$	$1$	$1$	$78.261$	$\Q$	None	✓				99.2.e.c	$1$	$0$	$2$	$0$	$-2$	$-4$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-2q^{5}-4q^{7}-4q^{10}+\cdots$
9801.2.a.m	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	$\Q(\sqrt{5}) $	None	✓				99.2.m.a	$1$	$1$	$-3$	$0$	$-2$	$2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+3\beta q^{4}-2\beta q^{5}+q^{7}+\cdots$
9801.2.a.n	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	$\Q(\sqrt{5}) $	None	✓				99.2.m.a	$1$	$1$	$-3$	$0$	$2$	$-2$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{2}+3\beta q^{4}+2\beta q^{5}-q^{7}+\cdots$
9801.2.a.o	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	$\Q(\sqrt{13}) $	None	✓				891.2.a.i	$1$	$0$	$-1$	$0$	$1$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(1+\beta )q^{4}+\beta q^{5}+(1-2\beta )q^{7}+\cdots$
9801.2.a.p	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	$\Q(\sqrt{33}) $	$\Q(\sqrt{-11}) $	✓				1089.2.e.f	$2$	$0$	$0$	$0$	$-3$	$0$	$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+(-1-\beta )q^{5}+4q^{16}+(2+2\beta )q^{20}+\cdots$
9801.2.a.q	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	$\Q(\sqrt{33}) $	$\Q(\sqrt{-11}) $	✓				1089.2.e.f	$2$	$1$	$0$	$0$	$3$	$0$	$+$	$+$	$+$	$1$	$N(\mathrm{U}(1))$	$q-2q^{4}+(1+\beta )q^{5}+4q^{16}+(-2-2\beta )q^{20}+\cdots$
9801.2.a.r	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	$\Q(\sqrt{3}) $	None	✓				1089.2.e.e	$2$	$1$	$0$	$0$	$-6$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-3q^{5}-2\beta q^{7}-\beta q^{8}+\cdots$
9801.2.a.s	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	$\Q(\sqrt{3}) $	None	✓	✓			9801.2.a.s	$2$	$1$	$0$	$0$	$-6$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-3q^{5}-\beta q^{8}-3\beta q^{10}+\cdots$
9801.2.a.t	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	$\Q(\sqrt{3}) $	None	✓	✓			9801.2.a.t	$1$	$0$	$0$	$0$	$0$	$-6$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-\beta q^{5}+(-3-\beta )q^{7}+\cdots$
9801.2.a.u	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	$\Q(\sqrt{3}) $	None	✓	✓			9801.2.a.t	$1$	$0$	$0$	$0$	$0$	$-6$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}-\beta q^{5}+(-3+\beta )q^{7}+\cdots$
9801.2.a.v	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	$\Q(\sqrt{3}) $	None	✓				81.2.a.a	$2$	$1$	$0$	$0$	$0$	$-4$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}+\beta q^{5}-2q^{7}-\beta q^{8}+\cdots$
9801.2.a.w	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	$\Q(\sqrt{3}) $	None	✓	✓			9801.2.a.t	$1$	$0$	$0$	$0$	$0$	$6$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}+\beta q^{5}+(3-\beta )q^{7}-\beta q^{8}+\cdots$
9801.2.a.x	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	$\Q(\sqrt{3}) $	None	✓	✓			9801.2.a.t	$1$	$0$	$0$	$0$	$0$	$6$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}+\beta q^{5}+(3+\beta )q^{7}-\beta q^{8}+\cdots$
9801.2.a.y	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	$\Q(\sqrt{3}) $	None	✓	✓			9801.2.a.s	$2$	$1$	$0$	$0$	$6$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}+3q^{5}-\beta q^{8}+3\beta q^{10}+\cdots$
9801.2.a.z	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	$\Q(\sqrt{3}) $	None	✓				1089.2.e.e	$2$	$0$	$0$	$0$	$6$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+q^{4}+3q^{5}+2\beta q^{7}-\beta q^{8}+\cdots$
9801.2.a.ba	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	$\Q(\sqrt{13}) $	None	✓				891.2.a.i	$1$	$0$	$1$	$0$	$-1$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{4}-\beta q^{5}+(1-2\beta )q^{7}+\cdots$
9801.2.a.bb	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	$\Q(\sqrt{5}) $	None	✓				99.2.m.a	$1$	$0$	$3$	$0$	$-2$	$-2$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+3\beta q^{4}-2\beta q^{5}-q^{7}+\cdots$
9801.2.a.bc	$9801$	$2$	9801.a	1.a	$1$	$2$	$2$	$78.261$	$\Q(\sqrt{5}) $	None	✓				99.2.m.a	$1$	$0$	$3$	$0$	$2$	$2$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}+3\beta q^{4}+2\beta q^{5}+q^{7}+\cdots$
9801.2.a.bd	$9801$	$2$	9801.a	1.a	$1$	$3$	$3$	$78.261$	$\Q(\zeta_{18})^+$	None	✓				99.2.e.d	$1$	$1$	$0$	$0$	$-3$	$3$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+(-1-\beta _{1})q^{5}+(1+\cdots)q^{7}+\cdots$
9801.2.a.be	$9801$	$2$	9801.a	1.a	$1$	$3$	$3$	$78.261$	$\Q(\zeta_{18})^+$	None	✓				99.2.e.d	$1$	$0$	$0$	$0$	$3$	$3$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1+\beta _{1})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
9801.2.a.bf	$9801$	$2$	9801.a	1.a	$1$	$3$	$3$	$78.261$	3.3.837.1	None	✓				891.2.a.m	$1$	$0$	$0$	$0$	$-6$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-2+\beta _{1})q^{5}+\cdots$
9801.2.a.bg	$9801$	$2$	9801.a	1.a	$1$	$3$	$3$	$78.261$	3.3.837.1	None	✓				891.2.a.m	$1$	$0$	$0$	$0$	$6$	$0$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(2-\beta _{1})q^{5}+\cdots$
9801.2.a.bh	$9801$	$2$	9801.a	1.a	$1$	$4$	$4$	$78.261$	4.4.4752.1	None	✓				891.2.a.o	$1$	$1$	$-2$	$0$	$8$	$2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(2+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
9801.2.a.bi	$9801$	$2$	9801.a	1.a	$1$	$4$	$4$	$78.261$	4.4.22545.1	None	✓				99.2.e.e	$1$	$0$	$-1$	$0$	$4$	$-1$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{2}+(3+\beta _{3})q^{4}+(1-\beta _{1}-\beta _{3})q^{5}+\cdots$
9801.2.a.bj	$9801$	$2$	9801.a	1.a	$1$	$4$	$4$	$78.261$	4.4.8112.1	None	✓	✓			9801.2.a.bj	$2$	$1$	$0$	$0$	$-2$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{2}q^{5}+\beta _{3}q^{7}+\cdots$
9801.2.a.bk	$9801$	$2$	9801.a	1.a	$1$	$4$	$4$	$78.261$	4.4.8112.1	None	✓	✓			9801.2.a.bj	$2$	$1$	$0$	$0$	$2$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{2}q^{5}-\beta _{3}q^{7}+\cdots$
9801.2.a.bl	$9801$	$2$	9801.a	1.a	$1$	$4$	$4$	$78.261$	4.4.22545.1	None	✓				99.2.e.e	$1$	$1$	$1$	$0$	$-4$	$-1$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{2}+(3+\beta _{3})q^{4}+(-1+\beta _{1}+\beta _{3})q^{5}+\cdots$
9801.2.a.bm	$9801$	$2$	9801.a	1.a	$1$	$4$	$4$	$78.261$	4.4.4752.1	None	✓				891.2.a.o	$1$	$1$	$2$	$0$	$-8$	$2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-2-\beta _{1}+\cdots)q^{5}+\cdots$
9801.2.a.bn	$9801$	$2$	9801.a	1.a	$1$	$5$	$5$	$78.261$	5.5.5144904.1	None	✓	✓			9801.2.a.bn	$1$	$0$	$-1$	$0$	$-4$	$3$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(-1+\beta _{3}+\cdots)q^{5}+\cdots$
9801.2.a.bo	$9801$	$2$	9801.a	1.a	$1$	$5$	$5$	$78.261$	5.5.5144904.1	None	✓	✓			9801.2.a.bn	$1$	$0$	$-1$	$0$	$4$	$-3$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(1-\beta _{3}+\cdots)q^{5}+\cdots$
9801.2.a.bp	$9801$	$2$	9801.a	1.a	$1$	$5$	$5$	$78.261$	5.5.5144904.1	None	✓	✓			9801.2.a.bn	$1$	$0$	$1$	$0$	$-4$	$-3$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(-1+\beta _{3}+\cdots)q^{5}+\cdots$
9801.2.a.bq	$9801$	$2$	9801.a	1.a	$1$	$5$	$5$	$78.261$	5.5.5144904.1	None	✓	✓			9801.2.a.bn	$1$	$0$	$1$	$0$	$4$	$3$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{1}+\beta _{2})q^{4}+(1-\beta _{3}+\cdots)q^{5}+\cdots$
9801.2.a.br	$9801$	$2$	9801.a	1.a	$1$	$6$	$6$	$78.261$	6.6.19783872.1	None	✓	✓			9801.2.a.br	$2$	$1$	$0$	$0$	$-8$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-1+\beta _{3})q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots$
9801.2.a.bs	$9801$	$2$	9801.a	1.a	$1$	$6$	$6$	$78.261$	6.6.19783872.1	None	✓	✓			9801.2.a.br	$2$	$1$	$0$	$0$	$8$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{3})q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots$
9801.2.a.bt	$9801$	$2$	9801.a	1.a	$1$	$6$	$6$	$78.261$	6.6.191244096.1	None	✓				1089.2.e.j	$2$	$1$	$0$	$0$	$-2$	$0$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{3}+\beta _{4})q^{4}-\beta _{3}q^{5}+\cdots$
9801.2.a.bu	$9801$	$2$	9801.a	1.a	$1$	$6$	$6$	$78.261$	6.6.191244096.1	None	✓				1089.2.e.j	$2$	$0$	$0$	$0$	$2$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{3}+\beta _{4})q^{4}+\beta _{3}q^{5}+\cdots$
9801.2.a.bv	$9801$	$2$	9801.a	1.a	$1$	$8$	$8$	$78.261$	8.8.$\cdots$.1	None	✓	✓			9801.2.a.bv	$2$	$1$	$0$	$0$	$0$	$-2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{6}q^{5}+\beta _{4}q^{7}+\cdots$
9801.2.a.bw	$9801$	$2$	9801.a	1.a	$1$	$8$	$8$	$78.261$	8.8.$\cdots$.1	None	✓	✓			9801.2.a.bv	$2$	$1$	$0$	$0$	$0$	$2$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{6}q^{5}-\beta _{4}q^{7}+\cdots$
9801.2.a.bx	$9801$	$2$	9801.a	1.a	$1$	$8$	$8$	$78.261$	8.8.$\cdots$.1	None	✓	✓			9801.2.a.bx	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{6}q^{2}+(1-\beta _{2}-\beta _{6}-\beta _{7})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$

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 70 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.