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 84 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
1062.2.a.a	$1062$	$2$	1062.a	1.a	$1$	$1$	$1$	$8.480$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{5}-q^{8}+4q^{10}+4q^{11}+\cdots$
1062.2.a.b	$1062$	$2$	1062.a	1.a	$1$	$1$	$1$	$8.480$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+3q^{7}-q^{8}+q^{10}+\cdots$
1062.2.a.c	$1062$	$2$	1062.a	1.a	$1$	$1$	$1$	$8.480$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{7}-q^{8}+4q^{11}-2q^{13}+\cdots$
1062.2.a.d	$1062$	$2$	1062.a	1.a	$1$	$1$	$1$	$8.480$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{8}-4q^{11}+4q^{13}+\cdots$
1062.2.a.e	$1062$	$2$	1062.a	1.a	$1$	$1$	$1$	$8.480$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-3q^{7}-q^{8}-2q^{10}+\cdots$
1062.2.a.f	$1062$	$2$	1062.a	1.a	$1$	$1$	$1$	$8.480$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{5}-q^{7}-q^{8}-4q^{10}+\cdots$
1062.2.a.g	$1062$	$2$	1062.a	1.a	$1$	$1$	$1$	$8.480$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}-3q^{7}+q^{8}-2q^{10}+\cdots$
1062.2.a.h	$1062$	$2$	1062.a	1.a	$1$	$1$	$1$	$8.480$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}-4q^{11}+\cdots$
1062.2.a.i	$1062$	$2$	1062.a	1.a	$1$	$1$	$1$	$8.480$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-4q^{7}+q^{8}-4q^{11}-2q^{13}+\cdots$
1062.2.a.j	$1062$	$2$	1062.a	1.a	$1$	$1$	$1$	$8.480$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{11}+5q^{13}+\cdots$
1062.2.a.k	$1062$	$2$	1062.a	1.a	$1$	$1$	$1$	$8.480$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{7}+q^{8}+5q^{11}+q^{13}+\cdots$
1062.2.a.l	$1062$	$2$	1062.a	1.a	$1$	$1$	$1$	$8.480$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+3q^{5}-q^{7}+q^{8}+3q^{10}+\cdots$
1062.2.a.m	$1062$	$2$	1062.a	1.a	$1$	$2$	$2$	$8.480$	$\Q(\sqrt{11}) $	None	✓	$1$	$0$	$2$	$0$	$-2$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1+\beta )q^{5}+4q^{7}+q^{8}+\cdots$
1062.2.a.n	$1062$	$2$	1062.a	1.a	$1$	$3$	$3$	$8.480$	3.3.316.1	None	✓	$1$	$0$	$-3$	$0$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots$
1062.2.a.o	$1062$	$2$	1062.a	1.a	$1$	$4$	$4$	$8.480$	4.4.106272.1	None	✓	$1$	$0$	$-4$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-\beta _{3}q^{5}-\beta _{2}q^{7}-q^{8}+\cdots$
1062.2.a.p	$1062$	$2$	1062.a	1.a	$1$	$4$	$4$	$8.480$	4.4.106272.1	None	✓	$1$	$0$	$4$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta _{3}q^{5}-\beta _{2}q^{7}+q^{8}+\cdots$
1062.2.c.a	$1062$	$2$	1062.c	177.d	$2$	$2$	$2$	$8.480$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$-2$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+\beta q^{5}-4q^{7}-q^{8}-\beta q^{10}+\cdots$
1062.2.c.b	$1062$	$2$	1062.c	177.d	$2$	$2$	$2$	$8.480$	$\Q(\sqrt{-2}) $	None		$2$	$1$	$2$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+\beta q^{5}-4q^{7}+q^{8}+\beta q^{10}+\cdots$
1062.2.c.c	$1062$	$2$	1062.c	177.d	$2$	$4$	$4$	$8.480$	$\Q(\sqrt{-2}, \sqrt{5})$	None		$2$	$0$	$-4$	$0$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+(1-\beta _{3})q^{7}+\cdots$
1062.2.c.d	$1062$	$2$	1062.c	177.d	$2$	$4$	$4$	$8.480$	$\Q(\sqrt{-2}, \sqrt{3})$	None		$2$	$0$	$-4$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+2\beta _{1}q^{5}+(2+\beta _{2})q^{7}+\cdots$
1062.2.c.e	$1062$	$2$	1062.c	177.d	$2$	$4$	$4$	$8.480$	$\Q(\sqrt{-2}, \sqrt{5})$	None		$2$	$0$	$4$	$0$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+(1-\beta _{3})q^{7}+\cdots$
1062.2.c.f	$1062$	$2$	1062.c	177.d	$2$	$4$	$4$	$8.480$	$\Q(\sqrt{-2}, \sqrt{3})$	None		$2$	$0$	$4$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+2\beta _{1}q^{5}+(2+\beta _{2})q^{7}+\cdots$
1062.2.e.a	$1062$	$2$	1062.e	9.c	$3$	$6$	$3$	$8.480$	6.0.309123.1	None		$2$	$0$	$-3$	$4$	$-2$	$7$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{2}+(-\beta _{2}-\beta _{3}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots$
1062.2.e.b	$1062$	$2$	1062.e	9.c	$3$	$6$	$3$	$8.480$	6.0.309123.1	None		$2$	$0$	$3$	$-2$	$-4$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{4}q^{2}+(\beta _{2}+\beta _{4})q^{3}+(-1-\beta _{4}+\cdots)q^{4}+\cdots$
1062.2.e.c	$1062$	$2$	1062.e	9.c	$3$	$6$	$3$	$8.480$	6.0.309123.1	None		$2$	$0$	$3$	$0$	$-4$	$6$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{4})q^{2}+(1-2\beta _{4})q^{3}-\beta _{4}q^{4}+\cdots$
1062.2.e.d	$1062$	$2$	1062.e	9.c	$3$	$14$	$7$	$8.480$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None		$2$	$0$	$7$	$1$	$4$	$0$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q+(1+\beta _{3})q^{2}-\beta _{1}q^{3}+\beta _{3}q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
1062.2.e.e	$1062$	$2$	1062.e	9.c	$3$	$26$	$13$	$8.480$		None		$2$	$0$	$-13$	$-3$	$-2$	$-12$			$\mathrm{SU}(2)[C_{3}]$
1062.2.e.f	$1062$	$2$	1062.e	9.c	$3$	$26$	$13$	$8.480$		None		$2$	$0$	$-13$	$1$	$6$	$5$			$\mathrm{SU}(2)[C_{3}]$
1062.2.e.g	$1062$	$2$	1062.e	9.c	$3$	$32$	$16$	$8.480$		None		$2$	$0$	$16$	$-1$	$6$	$-3$			$\mathrm{SU}(2)[C_{3}]$
1062.3.b.a	$1062$	$3$	1062.b	3.b	$2$	$16$	$16$	$28.937$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{8}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}-2q^{4}+\beta _{2}q^{5}-\beta _{10}q^{7}+\cdots$
1062.3.b.b	$1062$	$3$	1062.b	3.b	$2$	$20$	$20$	$28.937$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{10}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{14}q^{2}-2q^{4}+\beta _{1}q^{5}-\beta _{3}q^{7}+\cdots$
1062.3.d.a	$1062$	$3$	1062.d	59.b	$2$	$2$	$2$	$28.937$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$0$	$-8$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-2q^{4}-4q^{5}-4q^{7}-2\beta q^{8}+\cdots$
1062.3.d.b	$1062$	$3$	1062.d	59.b	$2$	$2$	$2$	$28.937$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$0$	$2$	$10$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-2q^{4}+q^{5}+5q^{7}-2\beta q^{8}+\cdots$
1062.3.d.c	$1062$	$3$	1062.d	59.b	$2$	$2$	$2$	$28.937$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$0$	$0$	$8$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-2q^{4}+4q^{5}-4q^{7}-2\beta q^{8}+\cdots$
1062.3.d.d	$1062$	$3$	1062.d	59.b	$2$	$8$	$8$	$28.937$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$0$	$0$	$-14$	$-18$		$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-2q^{4}+(-2-\beta _{2}+\beta _{4})q^{5}+\cdots$
1062.3.d.e	$1062$	$3$	1062.d	59.b	$2$	$16$	$16$	$28.937$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$24$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{11}q^{2}-2q^{4}+\beta _{1}q^{5}+(1-\beta _{5}+\cdots)q^{7}+\cdots$
1062.3.d.f	$1062$	$3$	1062.d	59.b	$2$	$20$	$20$	$28.937$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$8$		$2^{11}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}-2q^{4}-\beta _{5}q^{5}+\beta _{9}q^{7}+2\beta _{4}q^{8}+\cdots$
1062.4.a.a	$1062$	$4$	1062.a	1.a	$1$	$1$	$1$	$62.660$	$\Q$	None	✓	$1$	$1$	$-2$	$0$	$-14$	$-24$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}-14q^{5}-24q^{7}-8q^{8}+\cdots$
1062.4.a.b	$1062$	$4$	1062.a	1.a	$1$	$1$	$1$	$62.660$	$\Q$	None	✓	$1$	$0$	$-2$	$0$	$-5$	$-15$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}-5q^{5}-15q^{7}-8q^{8}+\cdots$
1062.4.a.c	$1062$	$4$	1062.a	1.a	$1$	$1$	$1$	$62.660$	$\Q$	None	✓	$1$	$0$	$-2$	$0$	$13$	$-27$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+13q^{5}-3^{3}q^{7}-8q^{8}+\cdots$
1062.4.a.d	$1062$	$4$	1062.a	1.a	$1$	$1$	$1$	$62.660$	$\Q$	None	✓	$1$	$0$	$2$	$0$	$5$	$-33$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+5q^{5}-33q^{7}+8q^{8}+\cdots$
1062.4.a.e	$1062$	$4$	1062.a	1.a	$1$	$1$	$1$	$62.660$	$\Q$	None	✓	$1$	$1$	$2$	$0$	$14$	$-24$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+14q^{5}-24q^{7}+8q^{8}+\cdots$
1062.4.a.f	$1062$	$4$	1062.a	1.a	$1$	$2$	$2$	$62.660$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$-4$	$0$	$20$	$-23$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+(11-2\beta )q^{5}+(-7+\cdots)q^{7}+\cdots$
1062.4.a.g	$1062$	$4$	1062.a	1.a	$1$	$2$	$2$	$62.660$	$\Q(\sqrt{51}) $	None	✓	$1$	$0$	$4$	$0$	$-26$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+(-13+\beta )q^{5}+4\beta q^{7}+\cdots$
1062.4.a.h	$1062$	$4$	1062.a	1.a	$1$	$2$	$2$	$62.660$	$\Q(\sqrt{21}) $	None	✓	$1$	$1$	$4$	$0$	$12$	$-23$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+(7-2\beta )q^{5}+(-13+\cdots)q^{7}+\cdots$
1062.4.a.i	$1062$	$4$	1062.a	1.a	$1$	$3$	$3$	$62.660$	3.3.47277.1	None	✓	$1$	$0$	$-6$	$0$	$18$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+4q^{4}+(6-\beta _{1}-\beta _{2})q^{5}+(2+\cdots)q^{7}+\cdots$
1062.4.a.j	$1062$	$4$	1062.a	1.a	$1$	$3$	$3$	$62.660$	3.3.45581.1	None	✓	$1$	$1$	$6$	$0$	$-4$	$13$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+(-2+\beta _{1}-\beta _{2})q^{5}+\cdots$
1062.4.a.k	$1062$	$4$	1062.a	1.a	$1$	$3$	$3$	$62.660$	3.3.13785.1	None	✓	$1$	$0$	$6$	$0$	$4$	$48$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+(1+\beta _{1}+\beta _{2})q^{5}+(15+\cdots)q^{7}+\cdots$
1062.4.a.l	$1062$	$4$	1062.a	1.a	$1$	$3$	$3$	$62.660$	3.3.30645.1	None	✓	$1$	$0$	$6$	$0$	$6$	$6$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+(2+\beta _{1}+2\beta _{2})q^{5}+\cdots$
1062.4.a.m	$1062$	$4$	1062.a	1.a	$1$	$3$	$3$	$62.660$	3.3.18989.1	None	✓	$1$	$0$	$6$	$0$	$28$	$26$	$+$	$3$	$\mathrm{SU}(2)$	$q+2q^{2}+4q^{4}+(9-\beta _{1}-\beta _{2})q^{5}+(8+\cdots)q^{7}+\cdots$

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 84 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.