LMFDB - Newform search results

Refine search

Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
		Only for weight 1:

				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	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	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1862.2.a.a	$1862$	$2$	1862.a	1.a	$1$	$1$	$1$	$14.868$	$\Q$	None	✓	$1$	$2$	$-1$	$-2$	$-3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}-3q^{5}+2q^{6}-q^{8}+\cdots$
1862.2.a.b	$1862$	$2$	1862.a	1.a	$1$	$1$	$1$	$14.868$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}-2q^{9}+\cdots$
1862.2.a.c	$1862$	$2$	1862.a	1.a	$1$	$1$	$1$	$14.868$	$\Q$	None	✓	$1$	$0$	$-1$	$2$	$3$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}+3q^{5}-2q^{6}-q^{8}+\cdots$
1862.2.a.d	$1862$	$2$	1862.a	1.a	$1$	$1$	$1$	$14.868$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}+q^{8}-3q^{9}-q^{10}+\cdots$
1862.2.a.e	$1862$	$2$	1862.a	1.a	$1$	$1$	$1$	$14.868$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}-3q^{9}+q^{10}+\cdots$
1862.2.a.f	$1862$	$2$	1862.a	1.a	$1$	$1$	$1$	$14.868$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}+q^{8}+\cdots$
1862.2.a.g	$1862$	$2$	1862.a	1.a	$1$	$2$	$2$	$14.868$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$-3$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-\beta )q^{3}+q^{4}+(-2+3\beta )q^{5}+\cdots$
1862.2.a.h	$1862$	$2$	1862.a	1.a	$1$	$2$	$2$	$14.868$	$\Q(\sqrt{29}) $	None	✓	$1$	$0$	$-2$	$-1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta q^{3}+q^{4}+(1-\beta )q^{5}+\beta q^{6}+\cdots$
1862.2.a.i	$1862$	$2$	1862.a	1.a	$1$	$2$	$2$	$14.868$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$-2$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}-q^{8}+\cdots$
1862.2.a.j	$1862$	$2$	1862.a	1.a	$1$	$2$	$2$	$14.868$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$-2$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta q^{3}+q^{4}+q^{5}-\beta q^{6}-q^{8}+\cdots$
1862.2.a.k	$1862$	$2$	1862.a	1.a	$1$	$2$	$2$	$14.868$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$-3$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-1-\beta )q^{3}+q^{4}-\beta q^{5}+(-1+\cdots)q^{6}+\cdots$
1862.2.a.l	$1862$	$2$	1862.a	1.a	$1$	$2$	$2$	$14.868$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$2$	$-1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta q^{3}+q^{4}+(-1+\beta )q^{5}-\beta q^{6}+\cdots$
1862.2.a.m	$1862$	$2$	1862.a	1.a	$1$	$2$	$2$	$14.868$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$2$	$3$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(1+\beta )q^{3}+q^{4}+\beta q^{5}+(1+\beta )q^{6}+\cdots$
1862.2.a.n	$1862$	$2$	1862.a	1.a	$1$	$3$	$3$	$14.868$	3.3.257.1	None	✓	$1$	$0$	$-3$	$-2$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}-2\beta _{1}q^{5}+\cdots$
1862.2.a.o	$1862$	$2$	1862.a	1.a	$1$	$3$	$3$	$14.868$	3.3.469.1	None	✓	$1$	$1$	$-3$	$-1$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{2}q^{3}+q^{4}-\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots$
1862.2.a.p	$1862$	$2$	1862.a	1.a	$1$	$3$	$3$	$14.868$	3.3.469.1	None	✓	$1$	$0$	$-3$	$1$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{1}q^{5}+\beta _{2}q^{6}+\cdots$
1862.2.a.q	$1862$	$2$	1862.a	1.a	$1$	$3$	$3$	$14.868$	3.3.257.1	None	✓	$1$	$0$	$-3$	$2$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+2\beta _{1}q^{5}+\cdots$
1862.2.a.r	$1862$	$2$	1862.a	1.a	$1$	$3$	$3$	$14.868$	3.3.469.1	None	✓	$1$	$0$	$3$	$1$	$-5$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{2}q^{3}+q^{4}+(-2+\beta _{1})q^{5}+\cdots$
1862.2.a.s	$1862$	$2$	1862.a	1.a	$1$	$4$	$4$	$14.868$	4.4.9792.1	None	✓	$1$	$1$	$-4$	$-2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{3})q^{5}+\cdots$
1862.2.a.t	$1862$	$2$	1862.a	1.a	$1$	$4$	$4$	$14.868$	4.4.9792.1	None	✓	$1$	$0$	$-4$	$2$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1+\beta _{3})q^{5}+\cdots$
1862.2.a.u	$1862$	$2$	1862.a	1.a	$1$	$4$	$4$	$14.868$	4.4.2624.1	None	✓	$1$	$1$	$4$	$-6$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(-2+\beta _{1})q^{3}+q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots$
1862.2.a.v	$1862$	$2$	1862.a	1.a	$1$	$4$	$4$	$14.868$	4.4.2624.1	None	✓	$1$	$0$	$4$	$6$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+(2-\beta _{1})q^{3}+q^{4}+(1-\beta _{2}+\beta _{3})q^{5}+\cdots$
1862.2.a.w	$1862$	$2$	1862.a	1.a	$1$	$5$	$5$	$14.868$	5.5.6530556.1	None	✓	$1$	$0$	$5$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots$
1862.2.a.x	$1862$	$2$	1862.a	1.a	$1$	$5$	$5$	$14.868$	5.5.6530556.1	None	✓	$1$	$0$	$5$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots$
1862.2.d.a	$1862$	$2$	1862.d	133.c	$2$	$24$	$24$	$14.868$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1862.2.d.b	$1862$	$2$	1862.d	133.c	$2$	$40$	$40$	$14.868$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1862.4.a.a	$1862$	$4$	1862.a	1.a	$1$	$1$	$1$	$109.862$	$\Q$	None	✓	$1$	$1$	$-2$	$2$	$9$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{3}+4q^{4}+9q^{5}-4q^{6}+\cdots$
1862.4.a.b	$1862$	$4$	1862.a	1.a	$1$	$2$	$2$	$109.862$	$\Q(\sqrt{177}) $	None	✓	$1$	$0$	$-4$	$-1$	$-10$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-\beta q^{3}+4q^{4}+(-6+2\beta )q^{5}+\cdots$
1862.4.a.c	$1862$	$4$	1862.a	1.a	$1$	$2$	$2$	$109.862$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-4$	$1$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(-1+3\beta )q^{3}+4q^{4}+(-3+\cdots)q^{5}+\cdots$
1862.4.a.d	$1862$	$4$	1862.a	1.a	$1$	$2$	$2$	$109.862$	$\Q(\sqrt{85}) $	None	✓	$1$	$1$	$-4$	$9$	$-12$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(5-\beta )q^{3}+4q^{4}+(-5-2\beta )q^{5}+\cdots$
1862.4.a.e	$1862$	$4$	1862.a	1.a	$1$	$2$	$2$	$109.862$	$\Q(\sqrt{73}) $	None	✓	$1$	$0$	$4$	$-9$	$9$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-4-\beta )q^{3}+4q^{4}+(3+3\beta )q^{5}+\cdots$
1862.4.a.f	$1862$	$4$	1862.a	1.a	$1$	$2$	$2$	$109.862$	$\Q(\sqrt{37}) $	None	✓	$1$	$1$	$4$	$3$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(1+\beta )q^{3}+4q^{4}+(3-2\beta )q^{5}+\cdots$
1862.4.a.g	$1862$	$4$	1862.a	1.a	$1$	$2$	$2$	$109.862$	$\Q(\sqrt{13}) $	None	✓	$1$	$0$	$4$	$7$	$14$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(2+3\beta )q^{3}+4q^{4}+(9-4\beta )q^{5}+\cdots$
1862.4.a.h	$1862$	$4$	1862.a	1.a	$1$	$4$	$4$	$109.862$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	$1$	$1$	$-8$	$-8$	$-7$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(-2+\beta _{1})q^{3}+4q^{4}+(-2+\cdots)q^{5}+\cdots$
1862.4.a.i	$1862$	$4$	1862.a	1.a	$1$	$4$	$4$	$109.862$	4.4.6939601.2	None	✓	$1$	$0$	$-8$	$6$	$-7$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+4q^{4}+(-2+\cdots)q^{5}+\cdots$
1862.4.a.j	$1862$	$4$	1862.a	1.a	$1$	$5$	$5$	$109.862$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	$1$	$1$	$10$	$-8$	$-21$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-2+\beta _{1})q^{3}+4q^{4}+(-4+\cdots)q^{5}+\cdots$
1862.4.a.k	$1862$	$4$	1862.a	1.a	$1$	$5$	$5$	$109.862$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	$1$	$0$	$10$	$6$	$-21$	$0$	$+$	$3$	$\mathrm{SU}(2)$	$q+2q^{2}+(1+\beta _{1})q^{3}+4q^{4}+(-4+\beta _{1}+\cdots)q^{5}+\cdots$
1862.4.a.l	$1862$	$4$	1862.a	1.a	$1$	$6$	$6$	$109.862$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$1$	$12$	$-9$	$-5$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(-1-\beta _{1})q^{3}+4q^{4}+(-1+\cdots)q^{5}+\cdots$
1862.4.a.m	$1862$	$4$	1862.a	1.a	$1$	$6$	$6$	$109.862$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	$1$	$0$	$12$	$9$	$5$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+(1+\beta _{1})q^{3}+4q^{4}+(1+\beta _{3}+\cdots)q^{5}+\cdots$
1862.4.a.n	$1862$	$4$	1862.a	1.a	$1$	$7$	$7$	$109.862$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$-14$	$-3$	$-5$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-\beta _{1}q^{3}+4q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
1862.4.a.o	$1862$	$4$	1862.a	1.a	$1$	$7$	$7$	$109.862$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$0$	$-14$	$3$	$5$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+\beta _{1}q^{3}+4q^{4}+(\beta _{1}+\beta _{2})q^{5}+\cdots$
1862.4.a.p	$1862$	$4$	1862.a	1.a	$1$	$7$	$7$	$109.862$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$14$	$-2$	$1$	$0$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+2q^{2}-\beta _{1}q^{3}+4q^{4}+(\beta _{1}+\beta _{6})q^{5}+\cdots$
1862.4.a.q	$1862$	$4$	1862.a	1.a	$1$	$7$	$7$	$109.862$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	$1$	$1$	$14$	$2$	$-1$	$0$	$-$	$2^{4}$	$\mathrm{SU}(2)$	$q+2q^{2}+\beta _{1}q^{3}+4q^{4}+(-\beta _{1}-\beta _{6})q^{5}+\cdots$
1862.4.a.r	$1862$	$4$	1862.a	1.a	$1$	$8$	$8$	$109.862$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-16$	$-2$	$7$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-2q^{2}-\beta _{1}q^{3}+4q^{4}+(1+\beta _{6})q^{5}+\cdots$
1862.4.a.s	$1862$	$4$	1862.a	1.a	$1$	$8$	$8$	$109.862$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$-16$	$2$	$-7$	$0$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-2q^{2}+\beta _{1}q^{3}+4q^{4}+(-1-\beta _{6}+\cdots)q^{5}+\cdots$
1862.4.a.t	$1862$	$4$	1862.a	1.a	$1$	$10$	$10$	$109.862$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$-20$	$-2$	$-7$	$0$	$+$	$2^{6}\cdot 3\cdot 7$	$\mathrm{SU}(2)$	$q-2q^{2}-\beta _{1}q^{3}+4q^{4}+(-1-\beta _{5}+\cdots)q^{5}+\cdots$
1862.4.a.u	$1862$	$4$	1862.a	1.a	$1$	$10$	$10$	$109.862$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$-20$	$2$	$7$	$0$	$+$	$2^{6}\cdot 3\cdot 7$	$\mathrm{SU}(2)$	$q-2q^{2}+\beta _{1}q^{3}+4q^{4}+(1+\beta _{5})q^{5}+\cdots$
1862.4.a.v	$1862$	$4$	1862.a	1.a	$1$	$11$	$11$	$109.862$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$0$	$22$	$-2$	$-13$	$0$	$+$	$2^{4}\cdot 3\cdot 7$	$\mathrm{SU}(2)$	$q+2q^{2}-\beta _{1}q^{3}+4q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots$
1862.4.a.w	$1862$	$4$	1862.a	1.a	$1$	$11$	$11$	$109.862$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$0$	$22$	$2$	$13$	$0$	$+$	$2^{4}\cdot 3\cdot 7$	$\mathrm{SU}(2)$	$q+2q^{2}+\beta _{1}q^{3}+4q^{4}+(1+\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots$
1862.4.a.x	$1862$	$4$	1862.a	1.a	$1$	$14$	$14$	$109.862$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$1$	$-28$	$-6$	$-10$	$0$	$-$	$7^{3}$	$\mathrm{SU}(2)$	$q-2q^{2}-\beta _{1}q^{3}+4q^{4}+(-1-\beta _{7}+\cdots)q^{5}+\cdots$

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.