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 213 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1950.2.a.a	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓	✓			1950.2.a.a	$1$	$0$	$-1$	$-1$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-3q^{7}-q^{8}+\cdots$
1950.2.a.b	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓		✓	✓	390.2.a.g	$1$	$1$	$-1$	$-1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots$
1950.2.a.c	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓		✓	✓	390.2.e.c	$1$	$1$	$-1$	$-1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots$
1950.2.a.d	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓				390.2.e.d	$1$	$0$	$-1$	$-1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+4q^{7}-q^{8}+\cdots$
1950.2.a.e	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓	✓			1950.2.a.e	$1$	$0$	$-1$	$-1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+4q^{7}-q^{8}+\cdots$
1950.2.a.f	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓	✓			1950.2.a.f	$1$	$0$	$-1$	$1$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-4q^{7}-q^{8}+\cdots$
1950.2.a.g	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓				390.2.e.b	$1$	$1$	$-1$	$1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-4q^{7}-q^{8}+\cdots$
1950.2.a.h	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓				390.2.a.e	$1$	$1$	$-1$	$1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-2q^{7}-q^{8}+\cdots$
1950.2.a.i	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓				390.2.e.a	$1$	$1$	$-1$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
1950.2.a.j	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓	✓			1950.2.a.j	$1$	$0$	$-1$	$1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
1950.2.a.k	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓				390.2.a.f	$1$	$0$	$-1$	$1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
1950.2.a.l	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓	✓			1950.2.a.l	$1$	$1$	$-1$	$1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots$
1950.2.a.m	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓	✓			1950.2.a.m	$1$	$1$	$-1$	$1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots$
1950.2.a.n	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓				390.2.a.c	$1$	$1$	$1$	$-1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots$
1950.2.a.o	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓				390.2.a.d	$1$	$0$	$1$	$-1$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots$
1950.2.a.p	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓	✓			1950.2.a.l	$1$	$1$	$1$	$-1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots$
1950.2.a.q	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓	✓			1950.2.a.m	$1$	$1$	$1$	$-1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots$
1950.2.a.r	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓				390.2.e.a	$1$	$0$	$1$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
1950.2.a.s	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓	✓			1950.2.a.j	$1$	$0$	$1$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
1950.2.a.t	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓	✓			1950.2.a.f	$1$	$0$	$1$	$-1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+4q^{7}+q^{8}+\cdots$
1950.2.a.u	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓				390.2.e.b	$1$	$0$	$1$	$-1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+4q^{7}+q^{8}+\cdots$
1950.2.a.v	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓		✓	✓	390.2.e.d	$1$	$1$	$1$	$1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-4q^{7}+q^{8}+\cdots$
1950.2.a.w	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓		✓	✓	78.2.a.a	$1$	$1$	$1$	$1$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-4q^{7}+q^{8}+\cdots$
1950.2.a.x	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓	✓			1950.2.a.e	$1$	$0$	$1$	$1$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-4q^{7}+q^{8}+\cdots$
1950.2.a.y	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓				390.2.a.a	$1$	$0$	$1$	$1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
1950.2.a.z	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓				390.2.e.c	$1$	$0$	$1$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots$
1950.2.a.ba	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓				390.2.a.b	$1$	$0$	$1$	$1$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots$
1950.2.a.bb	$1950$	$2$	1950.a	1.a	$1$	$1$	$1$	$15.571$	$\Q$	None	✓	✓			1950.2.a.a	$1$	$0$	$1$	$1$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+3q^{7}+q^{8}+\cdots$
1950.2.a.bc	$1950$	$2$	1950.a	1.a	$1$	$2$	$2$	$15.571$	$\Q(\sqrt{41}) $	None	✓	✓			1950.2.a.bc	$1$	$0$	$-2$	$-2$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+(-1-\beta )q^{7}+\cdots$
1950.2.a.bd	$1950$	$2$	1950.a	1.a	$1$	$2$	$2$	$15.571$	$\Q(\sqrt{2}) $	None	✓				390.2.a.h	$1$	$0$	$-2$	$-2$	$0$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}+\beta q^{7}-q^{8}+\cdots$
1950.2.a.be	$1950$	$2$	1950.a	1.a	$1$	$2$	$2$	$15.571$	$\Q(\sqrt{5}) $	None	✓		✓		390.2.e.e	$1$	$0$	$-2$	$2$	$0$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+(1+\beta )q^{7}+\cdots$
1950.2.a.bf	$1950$	$2$	1950.a	1.a	$1$	$2$	$2$	$15.571$	$\Q(\sqrt{5}) $	None	✓		✓		390.2.e.e	$1$	$1$	$2$	$-2$	$0$	$-2$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+(-1-\beta )q^{7}+\cdots$
1950.2.a.bg	$1950$	$2$	1950.a	1.a	$1$	$2$	$2$	$15.571$	$\Q(\sqrt{41}) $	None	✓	✓	✓		1950.2.a.bc	$1$	$0$	$2$	$2$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+(1+\beta )q^{7}+\cdots$
1950.2.b.a	$1950$	$2$	1950.b	13.b	$2$	$2$	$2$	$15.571$	$\Q(\sqrt{-1}) $	None		✓			1950.2.b.a	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}-q^{3}-q^{4}+iq^{6}+2iq^{7}+\cdots$
1950.2.b.b	$1950$	$2$	1950.b	13.b	$2$	$2$	$2$	$15.571$	$\Q(\sqrt{-1}) $	None		✓			1950.2.b.b	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-q^{3}-q^{4}-iq^{6}+3iq^{7}+\cdots$
1950.2.b.c	$1950$	$2$	1950.b	13.b	$2$	$2$	$2$	$15.571$	$\Q(\sqrt{-1}) $	None					78.2.b.a	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}-q^{3}-q^{4}+iq^{6}+2iq^{7}+\cdots$
1950.2.b.d	$1950$	$2$	1950.b	13.b	$2$	$2$	$2$	$15.571$	$\Q(\sqrt{-1}) $	None		✓			1950.2.b.b	$2$	$1$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+q^{3}-q^{4}+iq^{6}+3iq^{7}+\cdots$
1950.2.b.e	$1950$	$2$	1950.b	13.b	$2$	$2$	$2$	$15.571$	$\Q(\sqrt{-1}) $	None					390.2.b.b	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}+q^{3}-q^{4}-iq^{6}+iq^{8}+q^{9}+\cdots$
1950.2.b.f	$1950$	$2$	1950.b	13.b	$2$	$2$	$2$	$15.571$	$\Q(\sqrt{-1}) $	None		✓			1950.2.b.a	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}+q^{3}-q^{4}-iq^{6}+2iq^{7}+\cdots$
1950.2.b.g	$1950$	$2$	1950.b	13.b	$2$	$2$	$2$	$15.571$	$\Q(\sqrt{-1}) $	None					390.2.b.a	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+q^{3}-q^{4}+iq^{6}-iq^{8}+q^{9}+\cdots$
1950.2.b.h	$1950$	$2$	1950.b	13.b	$2$	$4$	$4$	$15.571$	$\Q(i, \sqrt{17})$	None					390.2.b.d	$2$	$0$	$0$	$-4$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-q^{3}-q^{4}+\beta _{1}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots$
1950.2.b.i	$1950$	$2$	1950.b	13.b	$2$	$4$	$4$	$15.571$	$\Q(i, \sqrt{17})$	None		✓			1950.2.b.i	$2$	$0$	$0$	$-4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-q^{3}-q^{4}-\beta _{2}q^{6}+(\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots$
1950.2.b.j	$1950$	$2$	1950.b	13.b	$2$	$4$	$4$	$15.571$	$\Q(i, \sqrt{17})$	None		✓			1950.2.b.i	$2$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+q^{3}-q^{4}+\beta _{2}q^{6}+(\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots$
1950.2.b.k	$1950$	$2$	1950.b	13.b	$2$	$4$	$4$	$15.571$	$\Q(i, \sqrt{13})$	None					390.2.b.c	$2$	$0$	$0$	$4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+q^{3}-q^{4}+\beta _{1}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots$
1950.2.b.l	$1950$	$2$	1950.b	13.b	$2$	$6$	$6$	$15.571$	6.0.350464.1	None					390.2.f.a	$2$	$0$	$0$	$-6$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}-q^{3}-q^{4}-\beta _{4}q^{6}+(\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots$
1950.2.b.m	$1950$	$2$	1950.b	13.b	$2$	$6$	$6$	$15.571$	6.0.350464.1	None					390.2.f.a	$2$	$0$	$0$	$6$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}+q^{3}-q^{4}+\beta _{4}q^{6}+(\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots$
1950.2.e.a	$1950$	$2$	1950.e	5.b	$2$	$2$	$2$	$15.571$	$\Q(\sqrt{-1}) $	None		✓			1950.2.a.l	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{7}+iq^{8}+\cdots$
1950.2.e.b	$1950$	$2$	1950.e	5.b	$2$	$2$	$2$	$15.571$	$\Q(\sqrt{-1}) $	None		✓			1950.2.a.m	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{7}+iq^{8}+\cdots$
1950.2.e.c	$1950$	$2$	1950.e	5.b	$2$	$2$	$2$	$15.571$	$\Q(\sqrt{-1}) $	None		✓			1950.2.a.f	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots$
1950.2.e.d	$1950$	$2$	1950.e	5.b	$2$	$2$	$2$	$15.571$	$\Q(\sqrt{-1}) $	None					390.2.a.d	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots$

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 213 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.