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 53 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
4056.2.a.a	$4056$	$2$	4056.a	1.a	$1$	$1$	$1$	$32.387$	$\Q$	None	✓				312.2.a.c	$1$	$1$	$0$	$-1$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-4q^{5}+q^{9}+2q^{11}+4q^{15}+\cdots$
4056.2.a.b	$4056$	$2$	4056.a	1.a	$1$	$1$	$1$	$32.387$	$\Q$	None	✓				312.2.q.c	$1$	$0$	$0$	$-1$	$-3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-3q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots$
4056.2.a.c	$4056$	$2$	4056.a	1.a	$1$	$1$	$1$	$32.387$	$\Q$	None	✓				312.2.q.b	$1$	$1$	$0$	$-1$	$-2$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+q^{7}+q^{9}-6q^{11}+2q^{15}+\cdots$
4056.2.a.d	$4056$	$2$	4056.a	1.a	$1$	$1$	$1$	$32.387$	$\Q$	None	✓				312.2.c.a	$1$	$0$	$0$	$-1$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{7}+q^{9}-2q^{11}-2q^{17}+\cdots$
4056.2.a.e	$4056$	$2$	4056.a	1.a	$1$	$1$	$1$	$32.387$	$\Q$	None	✓				312.2.c.a	$1$	$1$	$0$	$-1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}+q^{9}+2q^{11}-2q^{17}+\cdots$
4056.2.a.f	$4056$	$2$	4056.a	1.a	$1$	$1$	$1$	$32.387$	$\Q$	None	✓				312.2.a.b	$1$	$0$	$0$	$-1$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{7}+q^{9}+2q^{11}-6q^{17}+\cdots$
4056.2.a.g	$4056$	$2$	4056.a	1.a	$1$	$1$	$1$	$32.387$	$\Q$	None	✓				312.2.a.a	$1$	$0$	$0$	$-1$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}-4q^{7}+q^{9}-2q^{15}+\cdots$
4056.2.a.h	$4056$	$2$	4056.a	1.a	$1$	$1$	$1$	$32.387$	$\Q$	None	✓				312.2.q.b	$1$	$0$	$0$	$-1$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}-q^{7}+q^{9}+6q^{11}-2q^{15}+\cdots$
4056.2.a.i	$4056$	$2$	4056.a	1.a	$1$	$1$	$1$	$32.387$	$\Q$	None	✓				24.2.a.a	$1$	$1$	$0$	$-1$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+q^{9}-4q^{11}-2q^{15}+\cdots$
4056.2.a.j	$4056$	$2$	4056.a	1.a	$1$	$1$	$1$	$32.387$	$\Q$	None	✓				312.2.q.c	$1$	$1$	$0$	$-1$	$3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+3q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots$
4056.2.a.k	$4056$	$2$	4056.a	1.a	$1$	$1$	$1$	$32.387$	$\Q$	None	✓				312.2.c.c	$1$	$1$	$0$	$1$	$-4$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-4q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots$
4056.2.a.l	$4056$	$2$	4056.a	1.a	$1$	$1$	$1$	$32.387$	$\Q$	None	✓				312.2.q.a	$1$	$1$	$0$	$1$	$-3$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-3q^{5}+q^{9}-3q^{15}-q^{17}+\cdots$
4056.2.a.m	$4056$	$2$	4056.a	1.a	$1$	$1$	$1$	$32.387$	$\Q$	None	✓				312.2.a.f	$1$	$0$	$0$	$1$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+q^{9}-2q^{15}+2q^{17}+\cdots$
4056.2.a.n	$4056$	$2$	4056.a	1.a	$1$	$1$	$1$	$32.387$	$\Q$	None	✓				312.2.c.b	$1$	$0$	$0$	$1$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots$
4056.2.a.o	$4056$	$2$	4056.a	1.a	$1$	$1$	$1$	$32.387$	$\Q$	None	✓				312.2.a.e	$1$	$1$	$0$	$1$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{9}-6q^{11}+2q^{17}+4q^{23}+\cdots$
4056.2.a.p	$4056$	$2$	4056.a	1.a	$1$	$1$	$1$	$32.387$	$\Q$	None	✓				312.2.c.b	$1$	$1$	$0$	$1$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots$
4056.2.a.q	$4056$	$2$	4056.a	1.a	$1$	$1$	$1$	$32.387$	$\Q$	None	✓				312.2.q.a	$1$	$0$	$0$	$1$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}+q^{9}+3q^{15}-q^{17}+\cdots$
4056.2.a.r	$4056$	$2$	4056.a	1.a	$1$	$1$	$1$	$32.387$	$\Q$	None	✓				312.2.c.c	$1$	$0$	$0$	$1$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots$
4056.2.a.s	$4056$	$2$	4056.a	1.a	$1$	$1$	$1$	$32.387$	$\Q$	None	✓				312.2.a.d	$1$	$0$	$0$	$1$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{5}+4q^{7}+q^{9}+2q^{11}+\cdots$
4056.2.a.t	$4056$	$2$	4056.a	1.a	$1$	$2$	$2$	$32.387$	$\Q(\sqrt{3}) $	None	✓				312.2.bf.a	$1$	$1$	$0$	$-2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}+(-1+\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
4056.2.a.u	$4056$	$2$	4056.a	1.a	$1$	$2$	$2$	$32.387$	$\Q(\sqrt{3}) $	None	✓				312.2.bf.a	$1$	$0$	$0$	$-2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta q^{5}+(1+\beta )q^{7}+q^{9}+(1+\beta )q^{11}+\cdots$
4056.2.a.v	$4056$	$2$	4056.a	1.a	$1$	$2$	$2$	$32.387$	$\Q(\sqrt{13}) $	None	✓				312.2.q.d	$1$	$1$	$0$	$2$	$-2$	$2$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{3}-q^{5}+(1-\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots$
4056.2.a.w	$4056$	$2$	4056.a	1.a	$1$	$2$	$2$	$32.387$	$\Q(\sqrt{13}) $	None	✓				312.2.q.d	$1$	$0$	$0$	$2$	$2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+q^{5}+(-1-\beta )q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots$
4056.2.a.x	$4056$	$2$	4056.a	1.a	$1$	$3$	$3$	$32.387$	$\Q(\zeta_{14})^+$	None	✓	✓	✓		4056.2.a.x	$1$	$1$	$0$	$-3$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(-1-\beta _{2})q^{5}+(-1+2\beta _{1}+\cdots)q^{7}+\cdots$
4056.2.a.y	$4056$	$2$	4056.a	1.a	$1$	$3$	$3$	$32.387$	3.3.837.1	None	✓				312.2.q.e	$1$	$1$	$0$	$-3$	$0$	$-3$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{2}q^{5}+(-1+\beta _{1})q^{7}+q^{9}+\cdots$
4056.2.a.z	$4056$	$2$	4056.a	1.a	$1$	$3$	$3$	$32.387$	3.3.837.1	None	✓				312.2.q.e	$1$	$0$	$0$	$-3$	$0$	$3$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{2}q^{5}+(1-\beta _{1})q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots$
4056.2.a.ba	$4056$	$2$	4056.a	1.a	$1$	$3$	$3$	$32.387$	$\Q(\zeta_{14})^+$	None	✓	✓			4056.2.a.x	$1$	$1$	$0$	$-3$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+(1-\beta _{1})q^{5}+(-1+\beta _{1}-2\beta _{2})q^{7}+\cdots$
4056.2.a.bb	$4056$	$2$	4056.a	1.a	$1$	$3$	$3$	$32.387$	$\Q(\zeta_{14})^+$	None	✓	✓			4056.2.a.bb	$1$	$1$	$0$	$3$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1-2\beta _{1}+\beta _{2})q^{5}+(-1+2\beta _{1}+\cdots)q^{7}+\cdots$
4056.2.a.bc	$4056$	$2$	4056.a	1.a	$1$	$3$	$3$	$32.387$	$\Q(\zeta_{14})^+$	None	✓	✓	✓		4056.2.a.bb	$1$	$1$	$0$	$3$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(\beta _{1}+\beta _{2})q^{7}+\cdots$
4056.2.a.bd	$4056$	$2$	4056.a	1.a	$1$	$4$	$4$	$32.387$	4.4.25488.1	None	✓		✓		312.2.bf.b	$1$	$1$	$0$	$4$	$-4$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
4056.2.a.be	$4056$	$2$	4056.a	1.a	$1$	$4$	$4$	$32.387$	4.4.25488.1	None	✓				312.2.bf.b	$1$	$0$	$0$	$4$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+(1+\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
4056.2.a.bf	$4056$	$2$	4056.a	1.a	$1$	$6$	$6$	$32.387$	6.6.27700337.1	None	✓	✓	✓		4056.2.a.bf	$1$	$0$	$0$	$-6$	$-1$	$-7$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{5}q^{5}+(-1-\beta _{1})q^{7}+q^{9}+\cdots$
4056.2.a.bg	$4056$	$2$	4056.a	1.a	$1$	$6$	$6$	$32.387$	6.6.27700337.1	None	✓	✓	✓		4056.2.a.bf	$1$	$0$	$0$	$-6$	$1$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{5}q^{5}+(1+\beta _{1})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots$
4056.2.a.bh	$4056$	$2$	4056.a	1.a	$1$	$6$	$6$	$32.387$	6.6.27700337.1	None	✓	✓	✓		4056.2.a.bh	$1$	$0$	$0$	$6$	$-1$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(\beta _{1}-\beta _{3})q^{5}+(1-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots$
4056.2.a.bi	$4056$	$2$	4056.a	1.a	$1$	$6$	$6$	$32.387$	6.6.27700337.1	None	✓	✓	✓		4056.2.a.bh	$1$	$0$	$0$	$6$	$1$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(-1+\beta _{2}+\cdots)q^{7}+\cdots$
4056.2.c.a	$4056$	$2$	4056.c	13.b	$2$	$2$	$2$	$32.387$	$\Q(\sqrt{-1}) $	None					312.2.q.b	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+2 i q^{5}+i q^{7}+q^{9}-6 i q^{11}+\cdots$
4056.2.c.b	$4056$	$2$	4056.c	13.b	$2$	$2$	$2$	$32.387$	$\Q(\sqrt{-1}) $	None					312.2.q.c	$2$	$0$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+3 i q^{5}+4 i q^{7}+q^{9}-4 i q^{11}+\cdots$
4056.2.c.c	$4056$	$2$	4056.c	13.b	$2$	$2$	$2$	$32.387$	$\Q(\sqrt{-1}) $	None					312.2.a.a	$2$	$0$	$0$	$-2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+\beta q^{5}+2\beta q^{7}+q^{9}-\beta q^{15}+\cdots$
4056.2.c.d	$4056$	$2$	4056.c	13.b	$2$	$2$	$2$	$32.387$	$\Q(\sqrt{-1}) $	None					312.2.a.c	$2$	$0$	$0$	$-2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+2\beta q^{5}+q^{9}+\beta q^{11}-2\beta q^{15}+\cdots$
4056.2.c.e	$4056$	$2$	4056.c	13.b	$2$	$2$	$2$	$32.387$	$\Q(\sqrt{-1}) $	None					24.2.a.a	$2$	$0$	$0$	$-2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+\beta q^{5}+q^{9}+2\beta q^{11}-\beta q^{15}+\cdots$
4056.2.c.f	$4056$	$2$	4056.c	13.b	$2$	$2$	$2$	$32.387$	$\Q(\sqrt{-1}) $	None					312.2.a.b	$2$	$0$	$0$	$-2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+2\beta q^{7}+q^{9}+\beta q^{11}+6 q^{17}+\cdots$
4056.2.c.g	$4056$	$2$	4056.c	13.b	$2$	$2$	$2$	$32.387$	$\Q(\sqrt{-1}) $	None					312.2.a.e	$2$	$0$	$0$	$2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+q^{9}+3\beta q^{11}-2 q^{17}-4 q^{23}+\cdots$
4056.2.c.h	$4056$	$2$	4056.c	13.b	$2$	$2$	$2$	$32.387$	$\Q(\sqrt{-1}) $	None					312.2.a.f	$2$	$0$	$0$	$2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+\beta q^{5}+q^{9}+\beta q^{15}-2 q^{17}+\cdots$
4056.2.c.i	$4056$	$2$	4056.c	13.b	$2$	$2$	$2$	$32.387$	$\Q(\sqrt{-1}) $	None					312.2.q.a	$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+3 i q^{5}+q^{9}+3 i q^{15}+q^{17}+\cdots$
4056.2.c.j	$4056$	$2$	4056.c	13.b	$2$	$2$	$2$	$32.387$	$\Q(\sqrt{-1}) $	None					312.2.a.d	$2$	$0$	$0$	$2$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+2\beta q^{5}-2\beta q^{7}+q^{9}-\beta q^{11}+\cdots$
4056.2.c.k	$4056$	$2$	4056.c	13.b	$2$	$4$	$4$	$32.387$	$\Q(\zeta_{12})$	None					312.2.bf.a	$2$	$0$	$0$	$-4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-\beta_{2} q^{5}+(\beta_{2}-\beta_1)q^{7}+q^{9}+\cdots$
4056.2.c.l	$4056$	$2$	4056.c	13.b	$2$	$4$	$4$	$32.387$	$\Q(i, \sqrt{13})$	None					312.2.q.d	$2$	$0$	$0$	$4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots$
4056.2.c.m	$4056$	$2$	4056.c	13.b	$2$	$6$	$6$	$32.387$	6.0.44836416.1	None					312.2.q.e	$2$	$0$	$0$	$-6$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}-\beta _{4}q^{5}+(\beta _{1}+\beta _{5})q^{7}+q^{9}+\cdots$
4056.2.c.n	$4056$	$2$	4056.c	13.b	$2$	$6$	$6$	$32.387$	6.0.153664.1	None		✓			4056.2.a.x	$2$	$0$	$0$	$-6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{3}+(\beta _{3}+\beta _{5})q^{5}+(-2\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots$
4056.2.c.o	$4056$	$2$	4056.c	13.b	$2$	$6$	$6$	$32.387$	6.0.153664.1	None		✓			4056.2.a.bb	$2$	$0$	$0$	$6$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{3}+(\beta _{1}+\beta _{3})q^{5}+(\beta _{1}+\beta _{3})q^{7}+\cdots$

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 53 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.