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 30777 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
8001.2.a.a	$8001$	$2$	8001.a	1.a	$1$	$1$	$1$	$63.888$	$\Q$	None	✓	$1$	$2$	$-2$	$0$	$-3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-3q^{5}-q^{7}+6q^{10}+\cdots$
8001.2.a.b	$8001$	$2$	8001.a	1.a	$1$	$1$	$1$	$63.888$	$\Q$	None	✓	$1$	$2$	$-2$	$0$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-q^{5}-q^{7}+2q^{10}+\cdots$
8001.2.a.c	$8001$	$2$	8001.a	1.a	$1$	$1$	$1$	$63.888$	$\Q$	None	✓	$1$	$2$	$0$	$0$	$-3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-3q^{5}+q^{7}-6q^{11}-q^{13}+\cdots$
8001.2.a.d	$8001$	$2$	8001.a	1.a	$1$	$1$	$1$	$63.888$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-4$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-4q^{5}-q^{7}-3q^{8}-4q^{10}+\cdots$
8001.2.a.e	$8001$	$2$	8001.a	1.a	$1$	$1$	$1$	$63.888$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}+q^{7}-3q^{8}+2q^{13}+q^{14}+\cdots$
8001.2.a.f	$8001$	$2$	8001.a	1.a	$1$	$1$	$1$	$63.888$	$\Q$	None	✓	$1$	$1$	$2$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-q^{7}+2q^{13}-2q^{14}+\cdots$
8001.2.a.g	$8001$	$2$	8001.a	1.a	$1$	$1$	$1$	$63.888$	$\Q$	None	✓	$1$	$0$	$2$	$0$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+q^{5}-q^{7}+2q^{10}+\cdots$
8001.2.a.h	$8001$	$2$	8001.a	1.a	$1$	$2$	$2$	$63.888$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$-1$	$0$	$-3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(2+\beta )q^{4}+(-1-\beta )q^{5}-q^{7}+\cdots$
8001.2.a.i	$8001$	$2$	8001.a	1.a	$1$	$2$	$2$	$63.888$	$\Q(\sqrt{17}) $	None	✓	$1$	$1$	$0$	$0$	$3$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+(1+\beta )q^{5}-q^{7}+(2-2\beta )q^{11}+\cdots$
8001.2.a.j	$8001$	$2$	8001.a	1.a	$1$	$2$	$2$	$63.888$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$0$	$0$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}-\beta q^{5}+q^{7}-2\beta q^{8}-2q^{10}+\cdots$
8001.2.a.k	$8001$	$2$	8001.a	1.a	$1$	$2$	$2$	$63.888$	$\Q(\sqrt{6}) $	None	✓	$1$	$0$	$0$	$0$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+4q^{4}+\beta q^{5}+q^{7}+2\beta q^{8}+\cdots$
8001.2.a.l	$8001$	$2$	8001.a	1.a	$1$	$7$	$7$	$63.888$	7.7.118870813.1	None	✓	$1$	$1$	$2$	$0$	$8$	$7$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{4}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots$
8001.2.a.m	$8001$	$2$	8001.a	1.a	$1$	$11$	$11$	$63.888$	$\mathbb{Q}[x]/(x^{11} - \cdots)$	None	✓	$1$	$1$	$2$	$0$	$-1$	$-11$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{7}q^{5}-q^{7}+\cdots$
8001.2.a.n	$8001$	$2$	8001.a	1.a	$1$	$12$	$12$	$63.888$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$0$	$7$	$0$	$7$	$12$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{6}+\beta _{7})q^{4}+\cdots$
8001.2.a.o	$8001$	$2$	8001.a	1.a	$1$	$13$	$13$	$63.888$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$1$	$-4$	$0$	$-12$	$13$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{10}+\cdots)q^{5}+\cdots$
8001.2.a.p	$8001$	$2$	8001.a	1.a	$1$	$14$	$14$	$63.888$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$0$	$5$	$0$	$4$	$-14$	$-$	$5$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}-q^{7}+\cdots$
8001.2.a.q	$8001$	$2$	8001.a	1.a	$1$	$15$	$15$	$63.888$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	None	✓	$1$	$1$	$0$	$0$	$-7$	$-15$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{8}q^{5}-q^{7}+\cdots$
8001.2.a.r	$8001$	$2$	8001.a	1.a	$1$	$16$	$16$	$63.888$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$1$	$1$	$-5$	$0$	$1$	$-16$	$+$	$2^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{13}q^{5}-q^{7}+\cdots$
8001.2.a.s	$8001$	$2$	8001.a	1.a	$1$	$16$	$16$	$63.888$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$1$	$0$	$-4$	$0$	$-5$	$-16$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}-q^{7}+\cdots$
8001.2.a.t	$8001$	$2$	8001.a	1.a	$1$	$16$	$16$	$63.888$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$1$	$0$	$2$	$0$	$9$	$-16$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{11})q^{5}+\cdots$
8001.2.a.u	$8001$	$2$	8001.a	1.a	$1$	$18$	$18$	$63.888$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	$1$	$0$	$6$	$0$	$10$	$18$	$-$	$2\cdot 5$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{12})q^{5}+\cdots$
8001.2.a.v	$8001$	$2$	8001.a	1.a	$1$	$19$	$19$	$63.888$	$\mathbb{Q}[x]/(x^{19} - \cdots)$	None	✓	$1$	$0$	$-4$	$0$	$-5$	$19$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+q^{7}+\cdots$
8001.2.a.w	$8001$	$2$	8001.a	1.a	$1$	$20$	$20$	$63.888$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None	✓	$1$	$1$	$-8$	$0$	$-3$	$20$	$+$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{16}q^{5}+q^{7}+\cdots$
8001.2.a.x	$8001$	$2$	8001.a	1.a	$1$	$22$	$22$	$63.888$		None	✓	$2$	$1$	$0$	$0$	$0$	$22$	$+$		$\mathrm{SU}(2)$
8001.2.a.y	$8001$	$2$	8001.a	1.a	$1$	$28$	$28$	$63.888$		None	✓	$2$	$0$	$0$	$0$	$0$	$-28$	$-$		$\mathrm{SU}(2)$
8001.2.a.z	$8001$	$2$	8001.a	1.a	$1$	$32$	$32$	$63.888$		None	✓	$2$	$1$	$0$	$0$	$0$	$-32$	$+$		$\mathrm{SU}(2)$
8001.2.a.ba	$8001$	$2$	8001.a	1.a	$1$	$40$	$40$	$63.888$		None	✓	$2$	$0$	$0$	$0$	$0$	$40$	$-$		$\mathrm{SU}(2)$
8002.2.a.a	$8002$	$2$	8002.a	1.a	$1$	$1$	$1$	$63.896$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
8002.2.a.b	$8002$	$2$	8002.a	1.a	$1$	$1$	$1$	$63.896$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{8}-3q^{9}-2q^{11}+4q^{13}+\cdots$
8002.2.a.c	$8002$	$2$	8002.a	1.a	$1$	$1$	$1$	$63.896$	$\Q$	None	✓	$1$	$1$	$1$	$2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}-2q^{5}+2q^{6}+q^{8}+\cdots$
8002.2.a.d	$8002$	$2$	8002.a	1.a	$1$	$69$	$69$	$63.896$		None	✓	$1$	$1$	$69$	$-25$	$-33$	$-19$	$+$		$\mathrm{SU}(2)$
8002.2.a.e	$8002$	$2$	8002.a	1.a	$1$	$77$	$77$	$63.896$		None	✓	$1$	$0$	$-77$	$10$	$18$	$21$	$-$		$\mathrm{SU}(2)$
8002.2.a.f	$8002$	$2$	8002.a	1.a	$1$	$89$	$89$	$63.896$		None	✓	$1$	$1$	$-89$	$-12$	$-18$	$-27$	$+$		$\mathrm{SU}(2)$
8002.2.a.g	$8002$	$2$	8002.a	1.a	$1$	$95$	$95$	$63.896$		None	✓	$1$	$0$	$95$	$24$	$36$	$21$	$-$		$\mathrm{SU}(2)$
8003.2.a.a	$8003$	$2$	8003.a	1.a	$1$	$147$	$147$	$63.904$		None	✓	$1$	$1$	$-6$	$-23$	$-25$	$-33$	$+$		$\mathrm{SU}(2)$
8003.2.a.b	$8003$	$2$	8003.a	1.a	$1$	$153$	$153$	$63.904$		None	✓	$1$	$1$	$-9$	$-17$	$-31$	$-17$	$+$		$\mathrm{SU}(2)$
8003.2.a.c	$8003$	$2$	8003.a	1.a	$1$	$172$	$172$	$63.904$		None	✓	$1$	$0$	$8$	$25$	$27$	$31$	$-$		$\mathrm{SU}(2)$
8003.2.a.d	$8003$	$2$	8003.a	1.a	$1$	$179$	$179$	$63.904$		None	✓	$1$	$0$	$8$	$15$	$27$	$23$	$-$		$\mathrm{SU}(2)$
8004.2.a.a	$8004$	$2$	8004.a	1.a	$1$	$1$	$1$	$63.912$	$\Q$	None	✓	$1$	$1$	$0$	$-1$	$-2$	$-5$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}-5q^{7}+q^{9}-3q^{11}+\cdots$
8004.2.a.b	$8004$	$2$	8004.a	1.a	$1$	$1$	$1$	$63.912$	$\Q$	None	✓	$1$	$0$	$0$	$-1$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-2q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots$
8004.2.a.c	$8004$	$2$	8004.a	1.a	$1$	$1$	$1$	$63.912$	$\Q$	None	✓	$1$	$1$	$0$	$1$	$-2$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{5}+3q^{7}+q^{9}+3q^{11}+\cdots$
8004.2.a.d	$8004$	$2$	8004.a	1.a	$1$	$8$	$8$	$63.912$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$1$	$1$	$0$	$8$	$-5$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+(-1-\beta _{7})q^{5}+(\beta _{6}+\beta _{7})q^{7}+\cdots$
8004.2.a.e	$8004$	$2$	8004.a	1.a	$1$	$9$	$9$	$63.912$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$0$	$-9$	$-3$	$7$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{1}q^{5}+(1-\beta _{3})q^{7}+q^{9}+(\beta _{3}+\cdots)q^{11}+\cdots$
8004.2.a.f	$8004$	$2$	8004.a	1.a	$1$	$9$	$9$	$63.912$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	✓	$1$	$1$	$0$	$9$	$-1$	$-5$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{3}-\beta _{1}q^{5}+(-1-\beta _{6})q^{7}+q^{9}+\cdots$
8004.2.a.g	$8004$	$2$	8004.a	1.a	$1$	$12$	$12$	$63.912$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$1$	$1$	$0$	$-12$	$-3$	$4$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}-\beta _{1}q^{5}+\beta _{3}q^{7}+q^{9}-\beta _{2}q^{11}+\cdots$
8004.2.a.h	$8004$	$2$	8004.a	1.a	$1$	$13$	$13$	$63.912$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	None	✓	$1$	$0$	$0$	$-13$	$5$	$-8$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{1}q^{5}+(-1+\beta _{12})q^{7}+q^{9}+\cdots$
8004.2.a.i	$8004$	$2$	8004.a	1.a	$1$	$16$	$16$	$63.912$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$1$	$0$	$0$	$-16$	$5$	$-4$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{3}+\beta _{1}q^{5}-\beta _{12}q^{7}+q^{9}-\beta _{4}q^{11}+\cdots$
8004.2.a.j	$8004$	$2$	8004.a	1.a	$1$	$16$	$16$	$63.912$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$1$	$0$	$0$	$16$	$3$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{1}q^{5}-\beta _{7}q^{7}+q^{9}-\beta _{6}q^{11}+\cdots$
8004.2.a.k	$8004$	$2$	8004.a	1.a	$1$	$18$	$18$	$63.912$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None	✓	$1$	$0$	$0$	$18$	$5$	$6$	$-$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	$q+q^{3}+\beta _{1}q^{5}+\beta _{7}q^{7}+q^{9}-\beta _{9}q^{11}+\cdots$
8005.2.a.a	$8005$	$2$	8005.a	1.a	$1$	$1$	$1$	$63.920$	$\Q$	None	✓	$1$	$1$	$-1$	$-2$	$1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}-q^{4}+q^{5}+2q^{6}+2q^{7}+\cdots$

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 30777 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.