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
1870.2.a.a	$1870$	$2$	1870.a	1.a	$1$	$1$	$1$	$14.932$	$\Q$	None	✓	✓			1870.2.a.a	$1$	$0$	$-1$	$-3$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-3q^{3}+q^{4}-q^{5}+3q^{6}-q^{8}+\cdots$
1870.2.a.b	$1870$	$2$	1870.a	1.a	$1$	$1$	$1$	$14.932$	$\Q$	None	✓	✓			1870.2.a.b	$1$	$1$	$-1$	$-1$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots$
1870.2.a.c	$1870$	$2$	1870.a	1.a	$1$	$1$	$1$	$14.932$	$\Q$	None	✓	✓			1870.2.a.c	$1$	$0$	$-1$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-q^{8}-3q^{9}+q^{10}+\cdots$
1870.2.a.d	$1870$	$2$	1870.a	1.a	$1$	$1$	$1$	$14.932$	$\Q$	None	✓	✓			1870.2.a.d	$1$	$0$	$-1$	$0$	$1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-3q^{9}+\cdots$
1870.2.a.e	$1870$	$2$	1870.a	1.a	$1$	$1$	$1$	$14.932$	$\Q$	None	✓	✓			1870.2.a.e	$1$	$0$	$-1$	$1$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-4q^{7}+\cdots$
1870.2.a.f	$1870$	$2$	1870.a	1.a	$1$	$1$	$1$	$14.932$	$\Q$	None	✓	✓			1870.2.a.f	$1$	$1$	$-1$	$1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
1870.2.a.g	$1870$	$2$	1870.a	1.a	$1$	$1$	$1$	$14.932$	$\Q$	None	✓	✓			1870.2.a.g	$1$	$1$	$1$	$-3$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}+q^{4}+q^{5}-3q^{6}-4q^{7}+\cdots$
1870.2.a.h	$1870$	$2$	1870.a	1.a	$1$	$1$	$1$	$14.932$	$\Q$	None	✓	✓			1870.2.a.h	$1$	$1$	$1$	$-1$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots$
1870.2.a.i	$1870$	$2$	1870.a	1.a	$1$	$1$	$1$	$14.932$	$\Q$	None	✓	✓			1870.2.a.i	$1$	$0$	$1$	$1$	$1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots$
1870.2.a.j	$1870$	$2$	1870.a	1.a	$1$	$2$	$2$	$14.932$	$\Q(\sqrt{2}) $	None	✓	✓	✓	✓	1870.2.a.j	$1$	$1$	$-2$	$-2$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta )q^{3}+q^{4}+q^{5}+(1+\cdots)q^{6}+\cdots$
1870.2.a.k	$1870$	$2$	1870.a	1.a	$1$	$2$	$2$	$14.932$	$\Q(\sqrt{3}) $	None	✓	✓	✓	✓	1870.2.a.k	$1$	$0$	$-2$	$0$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}+q^{5}-\beta q^{6}+(1+\cdots)q^{7}+\cdots$
1870.2.a.l	$1870$	$2$	1870.a	1.a	$1$	$2$	$2$	$14.932$	$\Q(\sqrt{2}) $	None	✓	✓	✓	✓	1870.2.a.l	$1$	$1$	$2$	$-2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta )q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots$
1870.2.a.m	$1870$	$2$	1870.a	1.a	$1$	$2$	$2$	$14.932$	$\Q(\sqrt{17}) $	None	✓	✓	✓		1870.2.a.m	$1$	$0$	$2$	$1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta q^{3}+q^{4}+q^{5}+\beta q^{6}+q^{8}+\cdots$
1870.2.a.n	$1870$	$2$	1870.a	1.a	$1$	$3$	$3$	$14.932$	3.3.564.1	None	✓	✓	✓	✓	1870.2.a.n	$1$	$1$	$-3$	$1$	$-3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots$
1870.2.a.o	$1870$	$2$	1870.a	1.a	$1$	$3$	$3$	$14.932$	3.3.148.1	None	✓	✓	✓	✓	1870.2.a.o	$1$	$1$	$-3$	$1$	$3$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots$
1870.2.a.p	$1870$	$2$	1870.a	1.a	$1$	$3$	$3$	$14.932$	3.3.756.1	None	✓	✓	✓		1870.2.a.p	$1$	$0$	$-3$	$3$	$3$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots$
1870.2.a.q	$1870$	$2$	1870.a	1.a	$1$	$3$	$3$	$14.932$	3.3.148.1	None	✓	✓	✓	✓	1870.2.a.q	$1$	$1$	$3$	$-3$	$3$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{2})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots$
1870.2.a.r	$1870$	$2$	1870.a	1.a	$1$	$3$	$3$	$14.932$	3.3.940.1	None	✓	✓	✓	✓	1870.2.a.r	$1$	$0$	$3$	$0$	$-3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots$
1870.2.a.s	$1870$	$2$	1870.a	1.a	$1$	$4$	$4$	$14.932$	4.4.23252.1	None	✓	✓	✓	✓	1870.2.a.s	$1$	$1$	$4$	$-3$	$-4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots$
1870.2.a.t	$1870$	$2$	1870.a	1.a	$1$	$4$	$4$	$14.932$	4.4.17428.1	None	✓	✓	✓	✓	1870.2.a.t	$1$	$0$	$4$	$3$	$-4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1-\beta _{1})q^{3}+q^{4}-q^{5}+(1-\beta _{1}+\cdots)q^{6}+\cdots$
1870.2.a.u	$1870$	$2$	1870.a	1.a	$1$	$4$	$4$	$14.932$	4.4.25492.1	None	✓	✓	✓	✓	1870.2.a.u	$1$	$0$	$4$	$3$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta _{2})q^{3}+q^{4}+q^{5}+(1+\beta _{2}+\cdots)q^{6}+\cdots$
1870.2.a.v	$1870$	$2$	1870.a	1.a	$1$	$5$	$5$	$14.932$	5.5.3102944.1	None	✓	✓	✓	✓	1870.2.a.v	$1$	$0$	$-5$	$-1$	$-5$	$-8$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{3}q^{3}+q^{4}-q^{5}-\beta _{3}q^{6}+\cdots$
1870.2.b.a	$1870$	$2$	1870.b	5.b	$2$	$2$	$2$	$14.932$	$\Q(\sqrt{-1}) $	None		✓			1870.2.b.a	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}+2 i q^{3}-q^{4}+(-2 i+1)q^{5}+\cdots$
1870.2.b.b	$1870$	$2$	1870.b	5.b	$2$	$2$	$2$	$14.932$	$\Q(\sqrt{-1}) $	None		✓			1870.2.b.b	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}+2 i q^{3}-q^{4}+(-2 i+1)q^{5}+\cdots$
1870.2.b.c	$1870$	$2$	1870.b	5.b	$2$	$10$	$10$	$14.932$	10.0.$\cdots$.1	None		✓			1870.2.b.c	$2$	$0$	$0$	$0$	$2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+\beta _{9}q^{3}-q^{4}+(\beta _{1}+\beta _{7})q^{5}+\cdots$
1870.2.b.d	$1870$	$2$	1870.b	5.b	$2$	$14$	$14$	$14.932$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None		✓			1870.2.b.d	$2$	$0$	$0$	$0$	$-6$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{8}q^{2}-\beta _{1}q^{3}-q^{4}+(\beta _{4}+\beta _{7}+\beta _{11}+\cdots)q^{5}+\cdots$
1870.2.b.e	$1870$	$2$	1870.b	5.b	$2$	$26$	$26$	$14.932$		None		✓			1870.2.b.e	$2$	$0$	$0$	$0$	$-4$	$0$			$\mathrm{SU}(2)[C_{2}]$
1870.2.b.f	$1870$	$2$	1870.b	5.b	$2$	$26$	$26$	$14.932$		None		✓			1870.2.b.f	$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1870.2.c.a	$1870$	$2$	1870.c	17.b	$2$	$2$	$2$	$14.932$	$\Q(\sqrt{-1}) $	None		✓			1870.2.c.a	$2$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+i q^{5}+2 i q^{7}+q^{8}+\cdots$
1870.2.c.b	$1870$	$2$	1870.c	17.b	$2$	$12$	$12$	$14.932$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓			1870.2.c.b	$2$	$0$	$-12$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots$
1870.2.c.c	$1870$	$2$	1870.c	17.b	$2$	$12$	$12$	$14.932$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		✓			1870.2.c.c	$2$	$0$	$12$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\beta _{10}q^{3}+q^{4}+\beta _{6}q^{5}+\beta _{10}q^{6}+\cdots$
1870.2.c.d	$1870$	$2$	1870.c	17.b	$2$	$16$	$16$	$14.932$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓			1870.2.c.d	$2$	$0$	$16$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{7}q^{5}+\beta _{1}q^{6}+\cdots$
1870.2.c.e	$1870$	$2$	1870.c	17.b	$2$	$18$	$18$	$14.932$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None		✓	✓		1870.2.c.e	$2$	$0$	$-18$	$0$	$0$	$0$		$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{5}q^{5}-\beta _{1}q^{6}+\cdots$
1870.2.h.a	$1870$	$2$	1870.h	85.c	$2$	$46$	$46$	$14.932$		None		✓			1870.2.h.a	$2$	$0$	$0$	$-8$	$0$	$-8$			$\mathrm{SU}(2)[C_{2}]$
1870.2.h.b	$1870$	$2$	1870.h	85.c	$2$	$46$	$46$	$14.932$		None		✓			1870.2.h.a	$2$	$0$	$0$	$8$	$0$	$8$			$\mathrm{SU}(2)[C_{2}]$
1870.4.a.a	$1870$	$4$	1870.a	1.a	$1$	$1$	$1$	$110.334$	$\Q$	None	✓	✓			1870.4.a.a	$1$	$0$	$-2$	$1$	$5$	$26$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+q^{3}+4q^{4}+5q^{5}-2q^{6}+\cdots$
1870.4.a.b	$1870$	$4$	1870.a	1.a	$1$	$1$	$1$	$110.334$	$\Q$	None	✓	✓			1870.4.a.b	$1$	$1$	$2$	$-8$	$5$	$-16$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-8q^{3}+4q^{4}+5q^{5}-2^{4}q^{6}+\cdots$
1870.4.a.c	$1870$	$4$	1870.a	1.a	$1$	$8$	$8$	$110.334$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓	✓	1870.4.a.c	$1$	$1$	$-16$	$-4$	$-40$	$38$	$-$	$23$	$\mathrm{SU}(2)$	$q-2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots$
1870.4.a.d	$1870$	$4$	1870.a	1.a	$1$	$8$	$8$	$110.334$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓		1870.4.a.d	$1$	$1$	$16$	$-10$	$40$	$-20$	$-$	$3$	$\mathrm{SU}(2)$	$q+2q^{2}+(-1-\beta _{1})q^{3}+4q^{4}+5q^{5}+\cdots$
1870.4.a.e	$1870$	$4$	1870.a	1.a	$1$	$9$	$9$	$110.334$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓	✓	1870.4.a.e	$1$	$1$	$-18$	$-6$	$45$	$-19$	$-$	$2$	$\mathrm{SU}(2)$	$q-2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+5q^{5}+\cdots$
1870.4.a.f	$1870$	$4$	1870.a	1.a	$1$	$9$	$9$	$110.334$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓		1870.4.a.f	$1$	$0$	$-18$	$-1$	$45$	$8$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-2q^{2}-\beta _{1}q^{3}+4q^{4}+5q^{5}+2\beta _{1}q^{6}+\cdots$
1870.4.a.g	$1870$	$4$	1870.a	1.a	$1$	$9$	$9$	$110.334$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓	✓	1870.4.a.g	$1$	$1$	$18$	$-8$	$-45$	$-37$	$-$	$2$	$\mathrm{SU}(2)$	$q+2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots$
1870.4.a.h	$1870$	$4$	1870.a	1.a	$1$	$9$	$9$	$110.334$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	✓	✓	✓	1870.4.a.h	$1$	$0$	$18$	$10$	$-45$	$16$	$+$	$2$	$\mathrm{SU}(2)$	$q+2q^{2}+(1+\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots$
1870.4.a.i	$1870$	$4$	1870.a	1.a	$1$	$10$	$10$	$110.334$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓	✓	1870.4.a.i	$1$	$0$	$-20$	$-10$	$-50$	$-21$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots$
1870.4.a.j	$1870$	$4$	1870.a	1.a	$1$	$10$	$10$	$110.334$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓	✓	1870.4.a.j	$1$	$1$	$-20$	$-1$	$-50$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-\beta _{1}q^{3}+4q^{4}-5q^{5}+2\beta _{1}q^{6}+\cdots$
1870.4.a.k	$1870$	$4$	1870.a	1.a	$1$	$10$	$10$	$110.334$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓	✓	1870.4.a.k	$1$	$1$	$20$	$-15$	$50$	$-70$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-2+\beta _{1})q^{3}+4q^{4}+5q^{5}+\cdots$
1870.4.a.l	$1870$	$4$	1870.a	1.a	$1$	$10$	$10$	$110.334$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓	✓	1870.4.a.l	$1$	$0$	$20$	$0$	$50$	$17$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+\beta _{1}q^{3}+4q^{4}+5q^{5}+2\beta _{1}q^{6}+\cdots$
1870.4.a.m	$1870$	$4$	1870.a	1.a	$1$	$10$	$10$	$110.334$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓	✓	1870.4.a.m	$1$	$1$	$20$	$1$	$-50$	$19$	$-$	$3$	$\mathrm{SU}(2)$	$q+2q^{2}+\beta _{1}q^{3}+4q^{4}-5q^{5}+2\beta _{1}q^{6}+\cdots$
1870.4.a.n	$1870$	$4$	1870.a	1.a	$1$	$11$	$11$	$110.334$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	✓	✓	✓	1870.4.a.n	$1$	$0$	$-22$	$-7$	$-55$	$-21$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}-5q^{5}+\cdots$
1870.4.a.o	$1870$	$4$	1870.a	1.a	$1$	$11$	$11$	$110.334$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	✓	✓	✓	1870.4.a.o	$1$	$1$	$-22$	$3$	$55$	$9$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+\beta _{1}q^{3}+4q^{4}+5q^{5}-2\beta _{1}q^{6}+\cdots$

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 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.