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 66 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
1230.2.a.a	$1230$	$2$	1230.a	1.a	$1$	$1$	$1$	$9.822$	$\Q$	None	✓	✓	✓	✓	1230.2.a.a	$1$	$1$	$-1$	$-1$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots$
1230.2.a.b	$1230$	$2$	1230.a	1.a	$1$	$1$	$1$	$9.822$	$\Q$	None	✓	✓	✓	✓	1230.2.a.b	$1$	$0$	$-1$	$1$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$
1230.2.a.c	$1230$	$2$	1230.a	1.a	$1$	$1$	$1$	$9.822$	$\Q$	None	✓	✓	✓	✓	1230.2.a.c	$1$	$1$	$-1$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
1230.2.a.d	$1230$	$2$	1230.a	1.a	$1$	$1$	$1$	$9.822$	$\Q$	None	✓	✓	✓	✓	1230.2.a.d	$1$	$1$	$-1$	$1$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots$
1230.2.a.e	$1230$	$2$	1230.a	1.a	$1$	$1$	$1$	$9.822$	$\Q$	None	✓	✓	✓	✓	1230.2.a.e	$1$	$1$	$1$	$-1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-2q^{7}+\cdots$
1230.2.a.f	$1230$	$2$	1230.a	1.a	$1$	$1$	$1$	$9.822$	$\Q$	None	✓	✓			1230.2.a.f	$1$	$0$	$1$	$-1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
1230.2.a.g	$1230$	$2$	1230.a	1.a	$1$	$1$	$1$	$9.822$	$\Q$	None	✓	✓			1230.2.a.g	$1$	$0$	$1$	$-1$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+3q^{7}+\cdots$
1230.2.a.h	$1230$	$2$	1230.a	1.a	$1$	$1$	$1$	$9.822$	$\Q$	None	✓	✓	✓	✓	1230.2.a.h	$1$	$1$	$1$	$1$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-4q^{7}+\cdots$
1230.2.a.i	$1230$	$2$	1230.a	1.a	$1$	$1$	$1$	$9.822$	$\Q$	None	✓	✓			1230.2.a.i	$1$	$0$	$1$	$1$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots$
1230.2.a.j	$1230$	$2$	1230.a	1.a	$1$	$1$	$1$	$9.822$	$\Q$	None	✓	✓			1230.2.a.j	$1$	$0$	$1$	$1$	$-1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+3q^{7}+\cdots$
1230.2.a.k	$1230$	$2$	1230.a	1.a	$1$	$1$	$1$	$9.822$	$\Q$	None	✓	✓			1230.2.a.k	$1$	$0$	$1$	$1$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
1230.2.a.l	$1230$	$2$	1230.a	1.a	$1$	$2$	$2$	$9.822$	$\Q(\sqrt{17}) $	None	✓	✓	✓	✓	1230.2.a.l	$1$	$0$	$-2$	$-2$	$2$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(3-\beta )q^{7}+\cdots$
1230.2.a.m	$1230$	$2$	1230.a	1.a	$1$	$2$	$2$	$9.822$	$\Q(\sqrt{17}) $	None	✓	✓	✓	✓	1230.2.a.m	$1$	$0$	$-2$	$2$	$2$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(1+\beta )q^{7}+\cdots$
1230.2.a.n	$1230$	$2$	1230.a	1.a	$1$	$2$	$2$	$9.822$	$\Q(\sqrt{65}) $	None	✓	✓	✓	✓	1230.2.a.n	$1$	$0$	$2$	$-2$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+\beta q^{7}+\cdots$
1230.2.a.o	$1230$	$2$	1230.a	1.a	$1$	$2$	$2$	$9.822$	$\Q(\sqrt{5}) $	None	✓	✓	✓	✓	1230.2.a.o	$1$	$1$	$2$	$-2$	$2$	$-6$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(-3+\cdots)q^{7}+\cdots$
1230.2.a.p	$1230$	$2$	1230.a	1.a	$1$	$2$	$2$	$9.822$	$\Q(\sqrt{5}) $	None	✓	✓	✓		1230.2.a.p	$1$	$0$	$2$	$2$	$2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(1+\beta )q^{7}+\cdots$
1230.2.a.q	$1230$	$2$	1230.a	1.a	$1$	$4$	$4$	$9.822$	4.4.73108.1	None	✓	✓	✓	✓	1230.2.a.q	$1$	$0$	$-4$	$-4$	$-4$	$1$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-\beta _{2}q^{7}+\cdots$
1230.2.b.a	$1230$	$2$	1230.b	41.b	$2$	$2$	$2$	$9.822$	$\Q(\sqrt{-1}) $	None		✓			1230.2.b.a	$2$	$0$	$-2$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-i q^{3}+q^{4}+q^{5}+i q^{6}+\cdots$
1230.2.b.b	$1230$	$2$	1230.b	41.b	$2$	$2$	$2$	$9.822$	$\Q(\sqrt{-1}) $	None		✓			1230.2.b.b	$2$	$0$	$2$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-i q^{3}+q^{4}+q^{5}-i q^{6}+\cdots$
1230.2.b.c	$1230$	$2$	1230.b	41.b	$2$	$4$	$4$	$9.822$	$\Q(i, \sqrt{73})$	None		✓			1230.2.b.c	$2$	$0$	$-4$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta _{2}q^{3}+q^{4}+q^{5}-\beta _{2}q^{6}+\cdots$
1230.2.b.d	$1230$	$2$	1230.b	41.b	$2$	$6$	$6$	$9.822$	6.0.3356224.1	None		✓			1230.2.b.d	$2$	$0$	$6$	$0$	$-6$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
1230.2.b.e	$1230$	$2$	1230.b	41.b	$2$	$6$	$6$	$9.822$	6.0.153664.1	None		✓			1230.2.b.e	$2$	$0$	$6$	$0$	$6$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-\beta _{3}q^{3}+q^{4}+q^{5}-\beta _{3}q^{6}+\cdots$
1230.2.b.f	$1230$	$2$	1230.b	41.b	$2$	$8$	$8$	$9.822$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓	✓		1230.2.b.f	$2$	$0$	$-8$	$0$	$-8$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-\beta _{3}q^{3}+q^{4}-q^{5}+\beta _{3}q^{6}+\cdots$
1230.2.d.a	$1230$	$2$	1230.d	5.b	$2$	$2$	$2$	$9.822$	$\Q(\sqrt{-1}) $	None		✓			1230.2.d.a	$2$	$1$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}+i q^{3}-q^{4}+(i-2)q^{5}+\cdots$
1230.2.d.b	$1230$	$2$	1230.d	5.b	$2$	$2$	$2$	$9.822$	$\Q(\sqrt{-1}) $	None		✓			1230.2.d.b	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}+i q^{3}-q^{4}+(-2 i+1)q^{5}+\cdots$
1230.2.d.c	$1230$	$2$	1230.d	5.b	$2$	$2$	$2$	$9.822$	$\Q(\sqrt{-1}) $	None		✓			1230.2.d.c	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}+i q^{3}-q^{4}+(-2 i+1)q^{5}+\cdots$
1230.2.d.d	$1230$	$2$	1230.d	5.b	$2$	$2$	$2$	$9.822$	$\Q(\sqrt{-1}) $	None		✓			1230.2.d.d	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}+i q^{3}-q^{4}+(i+2)q^{5}+\cdots$
1230.2.d.e	$1230$	$2$	1230.d	5.b	$2$	$6$	$6$	$9.822$	6.0.350464.1	None		✓			1230.2.d.e	$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}-\beta _{4}q^{3}-q^{4}+(\beta _{2}-\beta _{5})q^{5}+\cdots$
1230.2.d.f	$1230$	$2$	1230.d	5.b	$2$	$12$	$12$	$9.822$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓			1230.2.d.f	$2$	$0$	$0$	$0$	$2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+\beta _{5}q^{3}-q^{4}-\beta _{7}q^{5}+q^{6}+\cdots$
1230.2.d.g	$1230$	$2$	1230.d	5.b	$2$	$14$	$14$	$9.822$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None		✓	✓		1230.2.d.g	$2$	$0$	$0$	$0$	$2$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{2}-\beta _{8}q^{3}-q^{4}+\beta _{11}q^{5}-q^{6}+\cdots$
1230.2.g.a	$1230$	$2$	1230.g	205.c	$2$	$22$	$22$	$9.822$		None		✓			1230.2.g.a	$2$	$0$	$0$	$-22$	$0$	$4$			$\mathrm{SU}(2)[C_{2}]$
1230.2.g.b	$1230$	$2$	1230.g	205.c	$2$	$22$	$22$	$9.822$		None		✓			1230.2.g.a	$2$	$0$	$0$	$22$	$0$	$-4$			$\mathrm{SU}(2)[C_{2}]$
1230.2.m.a	$1230$	$2$	1230.m	205.j	$4$	$40$	$20$	$9.822$		None		✓			1230.2.m.a	$2$	$0$	$-40$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
1230.2.m.b	$1230$	$2$	1230.m	205.j	$4$	$40$	$20$	$9.822$		None		✓			1230.2.m.a	$2$	$0$	$40$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{4}]$
1230.2.p.a	$1230$	$2$	1230.p	41.c	$4$	$4$	$2$	$9.822$	$\Q(\zeta_{8})$	None		✓			1230.2.p.a	$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+\zeta_{8}^{2}q^{5}+\cdots$
1230.2.p.b	$1230$	$2$	1230.p	41.c	$4$	$4$	$2$	$9.822$	$\Q(\zeta_{8})$	None		✓			1230.2.p.b	$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}^{2}q^{2}+\zeta_{8}^{3}q^{3}-q^{4}+\zeta_{8}^{2}q^{5}+\cdots$
1230.2.p.c	$1230$	$2$	1230.p	41.c	$4$	$4$	$2$	$9.822$	$\Q(\zeta_{8})$	None		✓			1230.2.p.c	$2$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}-\zeta_{8}^{2}q^{5}+\cdots$
1230.2.p.d	$1230$	$2$	1230.p	41.c	$4$	$4$	$2$	$9.822$	$\Q(\zeta_{8})$	None		✓			1230.2.p.d	$2$	$0$	$0$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}-\zeta_{8}^{2}q^{5}+\cdots$
1230.2.p.e	$1230$	$2$	1230.p	41.c	$4$	$8$	$4$	$9.822$	8.0.205520896.4	None		✓			1230.2.p.e	$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{2}-\beta _{1}q^{3}-q^{4}+\beta _{2}q^{5}+\beta _{5}q^{6}+\cdots$
1230.2.p.f	$1230$	$2$	1230.p	41.c	$4$	$8$	$4$	$9.822$	8.0.4328587264.1	None		✓			1230.2.p.f	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{2}+\beta _{5}q^{3}-q^{4}-\beta _{2}q^{5}-\beta _{3}q^{6}+\cdots$
1230.2.p.g	$1230$	$2$	1230.p	41.c	$4$	$8$	$4$	$9.822$	8.0.836829184.2	None		✓			1230.2.p.g	$2$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{7}q^{2}+\beta _{2}q^{3}-q^{4}-\beta _{7}q^{5}-\beta _{3}q^{6}+\cdots$
1230.2.p.h	$1230$	$2$	1230.p	41.c	$4$	$16$	$8$	$9.822$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓	✓		1230.2.p.h	$2$	$0$	$0$	$0$	$0$	$-8$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{10}q^{2}-\beta _{5}q^{3}-q^{4}+\beta _{10}q^{5}+\cdots$
1230.4.a.a	$1230$	$4$	1230.a	1.a	$1$	$1$	$1$	$72.572$	$\Q$	None	✓	✓			1230.4.a.a	$1$	$1$	$-2$	$-3$	$-5$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots$
1230.4.a.b	$1230$	$4$	1230.a	1.a	$1$	$1$	$1$	$72.572$	$\Q$	None	✓	✓			1230.4.a.b	$1$	$1$	$-2$	$-3$	$5$	$-16$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}+5q^{5}+6q^{6}+\cdots$
1230.4.a.c	$1230$	$4$	1230.a	1.a	$1$	$1$	$1$	$72.572$	$\Q$	None	✓	✓			1230.4.a.c	$1$	$0$	$-2$	$3$	$-5$	$13$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}-5q^{5}-6q^{6}+\cdots$
1230.4.a.d	$1230$	$4$	1230.a	1.a	$1$	$1$	$1$	$72.572$	$\Q$	None	✓	✓			1230.4.a.d	$1$	$0$	$2$	$3$	$5$	$16$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}+5q^{5}+6q^{6}+\cdots$
1230.4.a.e	$1230$	$4$	1230.a	1.a	$1$	$2$	$2$	$72.572$	$\Q(\sqrt{21}) $	None	✓	✓	✓		1230.4.a.e	$1$	$1$	$-4$	$-6$	$-10$	$-11$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}-5q^{5}+6q^{6}+\cdots$
1230.4.a.f	$1230$	$4$	1230.a	1.a	$1$	$3$	$3$	$72.572$	3.3.4853.1	None	✓	✓	✓	✓	1230.4.a.f	$1$	$1$	$6$	$9$	$15$	$-37$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}+5q^{5}+6q^{6}+\cdots$
1230.4.a.g	$1230$	$4$	1230.a	1.a	$1$	$4$	$4$	$72.572$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	✓	✓		1230.4.a.g	$1$	$1$	$-8$	$-12$	$20$	$-17$	$-$	$2$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}+5q^{5}+6q^{6}+\cdots$
1230.4.a.h	$1230$	$4$	1230.a	1.a	$1$	$4$	$4$	$72.572$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	✓	✓		1230.4.a.h	$1$	$0$	$-8$	$12$	$-20$	$-25$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}-5q^{5}-6q^{6}+\cdots$

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 66 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.