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 77 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
1210.2.a.a	$1210$	$2$	1210.a	1.a	$1$	$1$	$1$	$9.662$	$\Q$	None	✓	✓			1210.2.a.a	$1$	$1$	$-1$	$-3$	$-1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}+q^{4}-q^{5}+3q^{6}-5q^{7}+\cdots$
1210.2.a.b	$1210$	$2$	1210.a	1.a	$1$	$1$	$1$	$9.662$	$\Q$	None	✓				110.2.a.b	$1$	$1$	$-1$	$-1$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-3q^{7}+\cdots$
1210.2.a.c	$1210$	$2$	1210.a	1.a	$1$	$1$	$1$	$9.662$	$\Q$	None	✓	✓			1210.2.a.c	$1$	$1$	$-1$	$-1$	$1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+3q^{7}+\cdots$
1210.2.a.d	$1210$	$2$	1210.a	1.a	$1$	$1$	$1$	$9.662$	$\Q$	None	✓	✓			1210.2.a.d	$1$	$0$	$-1$	$-1$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+3q^{7}+\cdots$
1210.2.a.e	$1210$	$2$	1210.a	1.a	$1$	$1$	$1$	$9.662$	$\Q$	None	✓				110.2.a.c	$1$	$0$	$-1$	$1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots$
1210.2.a.f	$1210$	$2$	1210.a	1.a	$1$	$1$	$1$	$9.662$	$\Q$	None	✓	✓			1210.2.a.f	$1$	$1$	$-1$	$1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
1210.2.a.g	$1210$	$2$	1210.a	1.a	$1$	$1$	$1$	$9.662$	$\Q$	None	✓	✓			1210.2.a.g	$1$	$1$	$-1$	$2$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-q^{5}-2q^{6}-q^{8}+\cdots$
1210.2.a.h	$1210$	$2$	1210.a	1.a	$1$	$1$	$1$	$9.662$	$\Q$	None	✓	✓			1210.2.a.a	$1$	$0$	$1$	$-3$	$-1$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}+5q^{7}+\cdots$
1210.2.a.i	$1210$	$2$	1210.a	1.a	$1$	$1$	$1$	$9.662$	$\Q$	None	✓	✓	✓	✓	1210.2.a.d	$1$	$1$	$1$	$-1$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-3q^{7}+\cdots$
1210.2.a.j	$1210$	$2$	1210.a	1.a	$1$	$1$	$1$	$9.662$	$\Q$	None	✓	✓			1210.2.a.c	$1$	$0$	$1$	$-1$	$1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-3q^{7}+\cdots$
1210.2.a.k	$1210$	$2$	1210.a	1.a	$1$	$1$	$1$	$9.662$	$\Q$	None	✓				110.2.a.a	$1$	$1$	$1$	$1$	$-1$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-5q^{7}+\cdots$
1210.2.a.l	$1210$	$2$	1210.a	1.a	$1$	$1$	$1$	$9.662$	$\Q$	None	✓	✓			1210.2.a.f	$1$	$0$	$1$	$1$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
1210.2.a.m	$1210$	$2$	1210.a	1.a	$1$	$1$	$1$	$9.662$	$\Q$	None	✓	✓			1210.2.a.g	$1$	$0$	$1$	$2$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}-q^{5}+2q^{6}+q^{8}+\cdots$
1210.2.a.n	$1210$	$2$	1210.a	1.a	$1$	$2$	$2$	$9.662$	$\Q(\sqrt{5}) $	None	✓				110.2.g.b	$1$	$1$	$-2$	$-3$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-\beta )q^{3}+q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots$
1210.2.a.o	$1210$	$2$	1210.a	1.a	$1$	$2$	$2$	$9.662$	$\Q(\sqrt{3}) $	None	✓	✓			1210.2.a.o	$1$	$1$	$-2$	$0$	$-2$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}+(1+\cdots)q^{7}+\cdots$
1210.2.a.p	$1210$	$2$	1210.a	1.a	$1$	$2$	$2$	$9.662$	$\Q(\sqrt{5}) $	None	✓		✓		110.2.g.a	$1$	$0$	$-2$	$2$	$-2$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2\beta q^{3}+q^{4}-q^{5}-2\beta q^{6}+\cdots$
1210.2.a.q	$1210$	$2$	1210.a	1.a	$1$	$2$	$2$	$9.662$	$\Q(\sqrt{5}) $	None	✓		✓		110.2.g.b	$1$	$1$	$2$	$-3$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1-\beta )q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots$
1210.2.a.r	$1210$	$2$	1210.a	1.a	$1$	$2$	$2$	$9.662$	$\Q(\sqrt{33}) $	None	✓				110.2.a.d	$1$	$0$	$2$	$-1$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta q^{3}+q^{4}+q^{5}-\beta q^{6}-\beta q^{7}+\cdots$
1210.2.a.s	$1210$	$2$	1210.a	1.a	$1$	$2$	$2$	$9.662$	$\Q(\sqrt{3}) $	None	✓	✓			1210.2.a.o	$1$	$0$	$2$	$0$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+(-1+\cdots)q^{7}+\cdots$
1210.2.a.t	$1210$	$2$	1210.a	1.a	$1$	$2$	$2$	$9.662$	$\Q(\sqrt{5}) $	None	✓				110.2.g.a	$1$	$0$	$2$	$2$	$-2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2\beta q^{3}+q^{4}-q^{5}+2\beta q^{6}+\cdots$
1210.2.a.u	$1210$	$2$	1210.a	1.a	$1$	$4$	$4$	$9.662$	4.4.5225.1	None	✓		✓		110.2.g.c	$1$	$0$	$-4$	$3$	$4$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots$
1210.2.a.v	$1210$	$2$	1210.a	1.a	$1$	$4$	$4$	$9.662$	4.4.5225.1	None	✓		✓		110.2.g.c	$1$	$0$	$4$	$3$	$4$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+q^{5}+(1-\beta _{1}+\cdots)q^{6}+\cdots$
1210.2.b.a	$1210$	$2$	1210.b	5.b	$2$	$2$	$2$	$9.662$	$\Q(\sqrt{-1}) $	None					110.2.b.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}+i q^{3}-q^{4}+(i-2)q^{5}+\cdots$
1210.2.b.b	$1210$	$2$	1210.b	5.b	$2$	$2$	$2$	$9.662$	$\Q(\sqrt{-1}) $	None		✓			1210.2.b.b	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+3 i q^{3}-q^{4}+(-2 i-1)q^{5}+\cdots$
1210.2.b.c	$1210$	$2$	1210.b	5.b	$2$	$2$	$2$	$9.662$	$\Q(\sqrt{-1}) $	None		✓			1210.2.b.b	$2$	$1$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}+3 i q^{3}-q^{4}+(-2 i-1)q^{5}+\cdots$
1210.2.b.d	$1210$	$2$	1210.b	5.b	$2$	$2$	$2$	$9.662$	$\Q(\sqrt{-1}) $	None					110.2.b.b	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+2 i q^{3}-q^{4}+(2 i+1)q^{5}+\cdots$
1210.2.b.e	$1210$	$2$	1210.b	5.b	$2$	$2$	$2$	$9.662$	$\Q(\sqrt{-1}) $	None					110.2.b.c	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}+3 i q^{3}-q^{4}+(-i+2)q^{5}+\cdots$
1210.2.b.f	$1210$	$2$	1210.b	5.b	$2$	$4$	$4$	$9.662$	$\Q(i, \sqrt{5})$	None					110.2.j.a	$2$	$0$	$0$	$0$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+2\beta _{1}q^{3}-q^{4}+(-2-\beta _{3})q^{5}+\cdots$
1210.2.b.g	$1210$	$2$	1210.b	5.b	$2$	$4$	$4$	$9.662$	$\Q(i, \sqrt{5})$	None					110.2.j.a	$2$	$0$	$0$	$0$	$-8$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+2\beta _{1}q^{3}-q^{4}+(-2-\beta _{3})q^{5}+\cdots$
1210.2.b.h	$1210$	$2$	1210.b	5.b	$2$	$4$	$4$	$9.662$	$\Q(i, \sqrt{5})$	None		✓			1210.2.b.h	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{3}-q^{4}-\beta _{2}q^{5}-\beta _{3}q^{6}+\cdots$
1210.2.b.i	$1210$	$2$	1210.b	5.b	$2$	$4$	$4$	$9.662$	$\Q(\zeta_{12})$	None		✓			1210.2.b.i	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{12}^{3}q^{2}+(1-2\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots$
1210.2.b.j	$1210$	$2$	1210.b	5.b	$2$	$4$	$4$	$9.662$	$\Q(\zeta_{12})$	None		✓			1210.2.b.i	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{12}^{3}q^{2}+(1-2\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots$
1210.2.b.k	$1210$	$2$	1210.b	5.b	$2$	$8$	$8$	$9.662$	8.0.$\cdots$.1	None					110.2.j.b	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+(-\beta _{3}+\beta _{4})q^{3}-q^{4}+(1+\cdots)q^{5}+\cdots$
1210.2.b.l	$1210$	$2$	1210.b	5.b	$2$	$8$	$8$	$9.662$	8.0.$\cdots$.1	None					110.2.j.b	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}+(-\beta _{3}+\beta _{4})q^{3}-q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
1210.2.b.m	$1210$	$2$	1210.b	5.b	$2$	$8$	$8$	$9.662$	8.0.303595776.1	None		✓			1210.2.b.m	$4$	$0$	$0$	$0$	$6$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+(\beta _{2}-\beta _{4}+\beta _{6})q^{3}-q^{4}+\cdots$
1210.3.d.a	$1210$	$3$	1210.d	11.b	$2$	$4$	$4$	$32.970$	$\Q(\sqrt{-2}, \sqrt{5})$	None		✓			1210.3.d.a	$2$	$0$	$0$	$-4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-1-\beta _{3})q^{3}-2q^{4}+\beta _{3}q^{5}+\cdots$
1210.3.d.b	$1210$	$3$	1210.d	11.b	$2$	$4$	$4$	$32.970$	$\Q(\sqrt{-2}, \sqrt{5})$	None		✓			1210.3.d.b	$2$	$0$	$0$	$4$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(1-\beta _{3})q^{3}-2q^{4}-\beta _{3}q^{5}+\cdots$
1210.3.d.c	$1210$	$3$	1210.d	11.b	$2$	$16$	$16$	$32.970$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None					110.3.h.b	$2$	$0$	$0$	$-16$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{9}q^{2}+(-1+\beta _{2}-\beta _{3}+\beta _{4})q^{3}+\cdots$
1210.3.d.d	$1210$	$3$	1210.d	11.b	$2$	$16$	$16$	$32.970$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			1210.3.d.d	$2$	$0$	$0$	$-4$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{5}+\beta _{6})q^{3}-2q^{4}-\beta _{2}q^{5}+\cdots$
1210.3.d.e	$1210$	$3$	1210.d	11.b	$2$	$16$	$16$	$32.970$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓			1210.3.d.e	$2$	$0$	$0$	$4$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{4}q^{3}-2q^{4}+\beta _{10}q^{5}+\cdots$
1210.3.d.f	$1210$	$3$	1210.d	11.b	$2$	$16$	$16$	$32.970$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None					110.3.h.a	$2$	$0$	$0$	$24$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{2}+(1+\beta _{9})q^{3}-2q^{4}+(-1+\cdots)q^{5}+\cdots$
1210.4.a.a	$1210$	$4$	1210.a	1.a	$1$	$1$	$1$	$71.392$	$\Q$	None	✓				110.4.a.d	$1$	$1$	$-2$	$-8$	$-5$	$-26$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-8q^{3}+4q^{4}-5q^{5}+2^{4}q^{6}+\cdots$
1210.4.a.b	$1210$	$4$	1210.a	1.a	$1$	$1$	$1$	$71.392$	$\Q$	None	✓				10.4.a.a	$1$	$0$	$-2$	$-8$	$5$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-8q^{3}+4q^{4}+5q^{5}+2^{4}q^{6}+\cdots$
1210.4.a.c	$1210$	$4$	1210.a	1.a	$1$	$1$	$1$	$71.392$	$\Q$	None	✓	✓			1210.4.a.c	$1$	$0$	$-2$	$-5$	$-5$	$11$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-5q^{3}+4q^{4}-5q^{5}+10q^{6}+\cdots$
1210.4.a.d	$1210$	$4$	1210.a	1.a	$1$	$1$	$1$	$71.392$	$\Q$	None	✓				110.4.a.e	$1$	$1$	$-2$	$-4$	$-5$	$22$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-4q^{3}+4q^{4}-5q^{5}+8q^{6}+\cdots$
1210.4.a.e	$1210$	$4$	1210.a	1.a	$1$	$1$	$1$	$71.392$	$\Q$	None	✓				110.4.a.f	$1$	$0$	$-2$	$1$	$5$	$-23$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+4q^{4}+5q^{5}-2q^{6}+\cdots$
1210.4.a.f	$1210$	$4$	1210.a	1.a	$1$	$1$	$1$	$71.392$	$\Q$	None	✓	✓			1210.4.a.f	$1$	$0$	$-2$	$2$	$-5$	$-24$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{3}+4q^{4}-5q^{5}-4q^{6}+\cdots$
1210.4.a.g	$1210$	$4$	1210.a	1.a	$1$	$1$	$1$	$71.392$	$\Q$	None	✓				110.4.a.g	$1$	$1$	$-2$	$7$	$-5$	$-11$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+7q^{3}+4q^{4}-5q^{5}-14q^{6}+\cdots$
1210.4.a.h	$1210$	$4$	1210.a	1.a	$1$	$1$	$1$	$71.392$	$\Q$	None	✓				110.4.a.h	$1$	$0$	$-2$	$8$	$5$	$12$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+8q^{3}+4q^{4}+5q^{5}-2^{4}q^{6}+\cdots$
1210.4.a.i	$1210$	$4$	1210.a	1.a	$1$	$1$	$1$	$71.392$	$\Q$	None	✓				110.4.a.a	$1$	$1$	$2$	$-7$	$5$	$35$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-7q^{3}+4q^{4}+5q^{5}-14q^{6}+\cdots$

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 77 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.