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 1425 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				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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
1004.5.d.a	$1004$	$5$	1004.d	251.b	$2$	$14$	$14$	$103.783$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$\Q(\sqrt{-251}) $	✓	$2$	$0$	$0$	$0$	$0$	$0$	$2^{12}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q+(-\beta _{2}+\beta _{4}-\beta _{8})q^{3}+(2\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots$
1004.5.d.b	$1004$	$5$	1004.d	251.b	$2$	$70$	$70$	$103.783$		None		$2$	$0$	$0$	$2$	$-12$	$-110$		$\mathrm{SU}(2)[C_{2}]$
1008.5.d.a	$1008$	$5$	1008.d	3.b	$2$	$4$	$4$	$104.197$	$\Q(\sqrt{-2}, \sqrt{7})$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+2\beta _{2})q^{5}-7\beta _{3}q^{7}+(46\beta _{1}+29\beta _{2}+\cdots)q^{11}+\cdots$
1008.5.d.b	$1008$	$5$	1008.d	3.b	$2$	$4$	$4$	$104.197$	$\Q(\sqrt{-2}, \sqrt{7})$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2\cdot 3\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-4\beta _{1}+\beta _{2})q^{5}-\beta _{3}q^{7}+(-\beta _{1}+\cdots)q^{11}+\cdots$
1008.5.d.c	$1008$	$5$	1008.d	3.b	$2$	$8$	$8$	$104.197$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2^{4}\cdot 3^{7}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{7})q^{5}-\beta _{2}q^{7}+(4\beta _{1}+2\beta _{5}+\cdots)q^{11}+\cdots$
1008.5.d.d	$1008$	$5$	1008.d	3.b	$2$	$8$	$8$	$104.197$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2^{4}\cdot 3^{6}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-3\beta _{2}-\beta _{6})q^{5}+\beta _{1}q^{7}+(3\beta _{2}+\beta _{5}+\cdots)q^{11}+\cdots$
1008.5.d.e	$1008$	$5$	1008.d	3.b	$2$	$12$	$12$	$104.197$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2^{15}\cdot 3^{4}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{7}q^{5}-\beta _{3}q^{7}+(-7\beta _{5}-\beta _{7}-\beta _{10}+\cdots)q^{11}+\cdots$
1008.5.d.f	$1008$	$5$	1008.d	3.b	$2$	$12$	$12$	$104.197$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2^{15}\cdot 3^{6}\cdot 7^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2\beta _{3}-\beta _{5})q^{5}-\beta _{1}q^{7}+(7\beta _{3}-\beta _{5}+\cdots)q^{11}+\cdots$
1008.5.f.a	$1008$	$5$	1008.f	7.b	$2$	$1$	$1$	$104.197$	$\Q$	$\Q(\sqrt{-7}) $	✓	$2$	$0$	$0$	$0$	$0$	$-49$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-7^{2}q^{7}-206q^{11}-734q^{23}+5^{4}q^{25}+\cdots$
1008.5.f.b	$1008$	$5$	1008.f	7.b	$2$	$2$	$2$	$104.197$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $		$4$	$0$	$0$	$0$	$0$	$-94$	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+(-47+\zeta_{6})q^{7}+22\zeta_{6}q^{13}+52\zeta_{6}q^{19}+\cdots$
1008.5.f.c	$1008$	$5$	1008.f	7.b	$2$	$2$	$2$	$104.197$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$0$	$0$	$0$	$14$	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-3\zeta_{6}q^{5}+(7-7\zeta_{6})q^{7}+18q^{11}+\cdots$
1008.5.f.d	$1008$	$5$	1008.f	7.b	$2$	$2$	$2$	$104.197$	$\Q(\sqrt{7}) $	$\Q(\sqrt{-7}) $	✓	$4$	$0$	$0$	$0$	$0$	$98$	$2^{4}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q+7^{2}q^{7}+\beta q^{11}+6\beta q^{23}+5^{4}q^{25}+\cdots$
1008.5.f.e	$1008$	$5$	1008.f	7.b	$2$	$4$	$4$	$104.197$	$\Q(\sqrt{2}, \sqrt{-3})$	None		$4$	$0$	$0$	$0$	$0$	$-140$	$2^{9}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{5}+(-35-7\beta _{1})q^{7}-3\beta _{2}q^{11}+\cdots$
1008.5.f.f	$1008$	$5$	1008.f	7.b	$2$	$4$	$4$	$104.197$	$\Q(\sqrt{2}, \sqrt{-3})$	None		$2$	$0$	$0$	$0$	$0$	$-20$	$2^{7}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2\beta _{1}+\beta _{2})q^{5}+(-5+\beta _{1}+5\beta _{2}+\cdots)q^{7}+\cdots$
1008.5.f.g	$1008$	$5$	1008.f	7.b	$2$	$4$	$4$	$104.197$	$\Q(\sqrt{10}, \sqrt{-106})$	None		$4$	$0$	$0$	$0$	$0$	$-16$	$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{5}+(-4-\beta _{3})q^{7}-37\beta _{1}q^{11}+\cdots$
1008.5.f.h	$1008$	$5$	1008.f	7.b	$2$	$4$	$4$	$104.197$	4.0.1308672.3	None		$2$	$0$	$0$	$0$	$0$	$76$	$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{2})q^{5}+(19+\beta _{1}-\beta _{2}+3\beta _{3})q^{7}+\cdots$
1008.5.f.i	$1008$	$5$	1008.f	7.b	$2$	$4$	$4$	$104.197$	$\Q(\sqrt{-33}, \sqrt{-42})$	None		$4$	$0$	$0$	$0$	$0$	$112$	$2\cdot 3\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+(28+7\beta _{2})q^{7}-\beta _{3}q^{11}+\cdots$
1008.5.f.j	$1008$	$5$	1008.f	7.b	$2$	$6$	$6$	$104.197$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$-42$	$2^{6}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{5}+(-7-\beta _{1}+\beta _{4})q^{7}+(-38+\cdots)q^{11}+\cdots$
1008.5.f.k	$1008$	$5$	1008.f	7.b	$2$	$6$	$6$	$104.197$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$22$	$2^{6}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{5}+(3+2\beta _{1}+\beta _{2}+2\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots$
1008.5.f.l	$1008$	$5$	1008.f	7.b	$2$	$8$	$8$	$104.197$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$-56$	$2^{20}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{5}+(-7+\beta _{5})q^{7}+(-18-\beta _{5}+\cdots)q^{11}+\cdots$
1008.5.f.m	$1008$	$5$	1008.f	7.b	$2$	$16$	$16$	$104.197$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$56$	$2^{52}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+(3-\beta _{8})q^{7}+\beta _{11}q^{11}+\beta _{9}q^{13}+\cdots$
1008.5.f.n	$1008$	$5$	1008.f	7.b	$2$	$16$	$16$	$104.197$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$56$	$2^{48}\cdot 3^{4}\cdot 7$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{5}+(3-\beta _{4})q^{7}+(18-\beta _{9})q^{11}+\cdots$
1008.5.m.a	$1008$	$5$	1008.m	4.b	$2$	$4$	$4$	$104.197$	$\Q(\sqrt{-7}, \sqrt{13})$	None		$2$	$0$	$0$	$0$	$36$	$0$	$2^{4}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(9+\beta _{3})q^{5}+\beta _{2}q^{7}+(2\beta _{1}-4\beta _{2}+\cdots)q^{11}+\cdots$
1008.5.m.b	$1008$	$5$	1008.m	4.b	$2$	$8$	$8$	$104.197$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$0$	$0$	$-132$	$0$	$2^{16}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-17+\beta _{1})q^{5}-\beta _{4}q^{7}+(-2\beta _{3}+\cdots)q^{11}+\cdots$
1008.5.m.c	$1008$	$5$	1008.m	4.b	$2$	$8$	$8$	$104.197$	8.0.$\cdots$.1	None		$2$	$0$	$0$	$0$	$-48$	$0$	$2^{18}\cdot 3^{2}\cdot 5^{2}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-6-\beta _{4})q^{5}-\beta _{5}q^{7}+(5\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots$
1008.5.m.d	$1008$	$5$	1008.m	4.b	$2$	$8$	$8$	$104.197$	8.0.$\cdots$.4	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{20}\cdot 3^{4}\cdot 7^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{5}+\beta _{4}q^{7}-\beta _{5}q^{11}+(-106+\cdots)q^{13}+\cdots$
1008.5.m.e	$1008$	$5$	1008.m	4.b	$2$	$8$	$8$	$104.197$	8.0.$\cdots$.1	None		$2$	$0$	$0$	$0$	$36$	$0$	$2^{18}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(5+\beta _{3})q^{5}-\beta _{5}q^{7}+(7\beta _{1}+5\beta _{2}+\cdots)q^{11}+\cdots$
1008.5.m.f	$1008$	$5$	1008.m	4.b	$2$	$8$	$8$	$104.197$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$0$	$0$	$36$	$0$	$2^{16}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(4-\beta _{2})q^{5}+\beta _{7}q^{7}+(6\beta _{3}-2\beta _{4}+\cdots)q^{11}+\cdots$
1008.5.m.g	$1008$	$5$	1008.m	4.b	$2$	$16$	$16$	$104.197$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{52}\cdot 3^{8}\cdot 7^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{5}+\beta _{1}q^{7}+\beta _{5}q^{11}+(8+\beta _{6}+\cdots)q^{13}+\cdots$
1008.5.o.a	$1008$	$5$	1008.o	84.h	$2$	$24$	$24$	$104.197$		None		$8$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
1008.5.o.b	$1008$	$5$	1008.o	84.h	$2$	$40$	$40$	$104.197$		None		$8$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
1012.5.f.a	$1012$	$5$	1012.f	23.b	$2$	$80$	$80$	$104.610$		None		$2$	$0$	$0$	$10$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
1012.5.h.a	$1012$	$5$	1012.h	11.b	$2$	$88$	$88$	$104.610$		None		$2$	$0$	$0$	$16$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
1020.5.i.a	$1020$	$5$	1020.i	51.c	$2$	$96$	$96$	$105.437$		None		$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
1020.5.m.a	$1020$	$5$	1020.m	3.b	$2$	$84$	$84$	$105.437$		None		$2$	$0$	$0$	$0$	$0$	$-216$		$\mathrm{SU}(2)[C_{2}]$
1026.5.c.a	$1026$	$5$	1026.c	3.b	$2$	$24$	$24$	$106.058$		None		$2$	$0$	$0$	$0$	$0$	$80$		$\mathrm{SU}(2)[C_{2}]$
1026.5.c.b	$1026$	$5$	1026.c	3.b	$2$	$24$	$24$	$106.058$		None		$2$	$0$	$0$	$0$	$0$	$80$		$\mathrm{SU}(2)[C_{2}]$
1026.5.c.c	$1026$	$5$	1026.c	3.b	$2$	$48$	$48$	$106.058$		None		$2$	$0$	$0$	$0$	$0$	$-80$		$\mathrm{SU}(2)[C_{2}]$
1032.5.e.a	$1032$	$5$	1032.e	43.b	$2$	$88$	$88$	$106.678$		None		$2$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
1036.5.c.a	$1036$	$5$	1036.c	7.b	$2$	$96$	$96$	$107.091$		None		$2$	$0$	$0$	$0$	$0$	$110$		$\mathrm{SU}(2)[C_{2}]$
1036.5.e.a	$1036$	$5$	1036.e	259.b	$2$	$2$	$2$	$107.091$	$\Q(\sqrt{777}) $	$\Q(\sqrt{-259}) $	✓	$2$	$0$	$0$	$0$	$-13$	$98$	$3$	$\mathrm{U}(1)[D_{2}]$	$q+(-6+\beta )q^{5}+7^{2}q^{7}+3^{4}q^{9}+(6+\cdots)q^{11}+\cdots$
1036.5.e.b	$1036$	$5$	1036.e	259.b	$2$	$2$	$2$	$107.091$	$\Q(\sqrt{777}) $	$\Q(\sqrt{-259}) $	✓	$2$	$0$	$0$	$0$	$13$	$98$	$3$	$\mathrm{U}(1)[D_{2}]$	$q+(7+\beta )q^{5}+7^{2}q^{7}+3^{4}q^{9}+(11+5\beta )q^{11}+\cdots$
1036.5.e.c	$1036$	$5$	1036.e	259.b	$2$	$4$	$4$	$107.091$	$\Q(\sqrt{3}, \sqrt{259})$	$\Q(\sqrt{-259}) $	✓	$4$	$0$	$0$	$0$	$0$	$-196$	$2^{3}\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+(-\beta _{1}+\beta _{2})q^{5}-7^{2}q^{7}+3^{4}q^{9}+\cdots$
1036.5.e.d	$1036$	$5$	1036.e	259.b	$2$	$92$	$92$	$107.091$		None		$4$	$0$	$0$	$0$	$0$	$-82$		$\mathrm{SU}(2)[C_{2}]$
1040.5.c.a	$1040$	$5$	1040.c	4.b	$2$	$32$	$32$	$107.505$		None		$2$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
1040.5.c.b	$1040$	$5$	1040.c	4.b	$2$	$64$	$64$	$107.505$		None		$2$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
1044.5.d.a	$1044$	$5$	1044.d	3.b	$2$	$36$	$36$	$107.918$		None		$2$	$0$	$0$	$0$	$0$	$-112$		$\mathrm{SU}(2)[C_{2}]$
1044.5.e.a	$1044$	$5$	1044.e	87.d	$2$	$40$	$40$	$107.918$		None		$4$	$0$	$0$	$0$	$0$	$-160$		$\mathrm{SU}(2)[C_{2}]$
1044.5.k.a	$1044$	$5$	1044.k	29.c	$4$	$20$	$10$	$107.918$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$	$2^{13}$	$\mathrm{SU}(2)[C_{4}]$	$q+(2\beta _{2}+\beta _{10})q^{5}+(\beta _{1}+\beta _{3}-\beta _{8})q^{7}+\cdots$
1044.5.k.b	$1044$	$5$	1044.k	29.c	$4$	$40$	$20$	$107.918$		None		$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{4}]$

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 1425 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.