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 199 matches)

Next Download displayed columns for results to

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	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	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
135.1.d.a	$135$	$1$	135.d	15.d	$2$	$1$	$1$	$0.067$	$\Q$	$D_{3}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$0$	$-1$	$0$	$1$	$0$		$1$		$q-q^{2}+q^{5}+q^{8}-q^{10}-q^{16}-q^{17}+\cdots$
135.1.d.b	$135$	$1$	135.d	15.d	$2$	$1$	$1$	$0.067$	$\Q$	$D_{3}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$0$	$1$	$0$	$-1$	$0$		$1$		$q+q^{2}-q^{5}-q^{8}-q^{10}-q^{16}+q^{17}+\cdots$
135.2.a.a	$135$	$2$	135.a	1.a	$1$	$1$	$1$	$1.078$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-q^{5}-3q^{7}+2q^{10}+\cdots$
135.2.a.b	$135$	$2$	135.a	1.a	$1$	$1$	$1$	$1.078$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+q^{5}-3q^{7}+2q^{10}+\cdots$
135.2.a.c	$135$	$2$	135.a	1.a	$1$	$2$	$2$	$1.078$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(1+\beta )q^{4}+q^{5}+(2-2\beta )q^{7}+\cdots$
135.2.a.d	$135$	$2$	135.a	1.a	$1$	$2$	$2$	$1.078$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{4}-q^{5}+(2-2\beta )q^{7}+\cdots$
135.2.b.a	$135$	$2$	135.b	5.b	$2$	$4$	$4$	$1.078$	$\Q(i, \sqrt{5})$	$_{}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{2}+(-2+\beta _{3})q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
135.2.b.b	$135$	$2$	135.b	5.b	$2$	$4$	$4$	$1.078$	$\Q(\zeta_{8})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{8}^{2}q^{2}+\zeta_{8}^{3}q^{5}-\zeta_{8}q^{7}+2\zeta_{8}^{2}q^{8}+\cdots$
135.2.e.a	$135$	$2$	135.e	9.c	$3$	$2$	$1$	$1.078$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$1$	$0$	$-1$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+\cdots$
135.2.e.b	$135$	$2$	135.e	9.c	$3$	$6$	$3$	$1.078$	6.0.954288.1	$_{}$	None	None		$2$	$0$	$1$	$0$	$3$	$-5$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{4}+\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
135.2.f.a	$135$	$2$	135.f	15.e	$4$	$8$	$4$	$1.078$	8.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+(\beta _{4}+\beta _{6})q^{4}+(-\beta _{3}-\beta _{5}+\cdots)q^{5}+\cdots$
135.2.f.b	$135$	$2$	135.f	15.e	$4$	$8$	$4$	$1.078$	8.0.$\cdots$.8	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+(2\beta _{2}+\beta _{3}+\beta _{6})q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots$
135.2.j.a	$135$	$2$	135.j	45.j	$6$	$8$	$4$	$1.078$	$\Q(\zeta_{24})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{24}^{6}q^{2}-\zeta_{24}^{3}q^{4}+(\zeta_{24}-\zeta_{24}^{3}+\cdots)q^{5}+\cdots$
135.2.k.a	$135$	$2$	135.k	27.e	$9$	$30$	$5$	$1.078$		$_{}$	None	None		$2$	$0$	$0$	$3$	$0$	$0$			$\mathrm{SU}(2)[C_{9}]$
135.2.k.b	$135$	$2$	135.k	27.e	$9$	$42$	$7$	$1.078$		$_{}$	None	None		$2$	$0$	$0$	$-3$	$0$	$0$			$\mathrm{SU}(2)[C_{9}]$
135.2.m.a	$135$	$2$	135.m	45.l	$12$	$16$	$4$	$1.078$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$6$	$0$	$6$	$-2$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+\beta _{5}q^{2}+(\beta _{5}+\beta _{8}+\beta _{15})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
135.2.p.a	$135$	$2$	135.p	135.p	$18$	$96$	$16$	$1.078$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-9$	$0$			$\mathrm{SU}(2)[C_{18}]$
135.2.q.a	$135$	$2$	135.q	135.q	$36$	$192$	$16$	$1.078$		$_{}$	None	None		$4$	$0$	$-12$	$-12$	$-12$	$-12$			$\mathrm{SU}(2)[C_{36}]$
135.3.c.a	$135$	$3$	135.c	3.b	$2$	$2$	$2$	$3.678$	$\Q(\sqrt{-5}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$24$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-q^{4}-\beta q^{5}+12q^{7}+3\beta q^{8}+\cdots$
135.3.c.b	$135$	$3$	135.c	3.b	$2$	$4$	$4$	$3.678$	$\Q(\sqrt{-5}, \sqrt{-29})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-14$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-5+\beta _{3})q^{4}+\beta _{2}q^{5}+(-4+\cdots)q^{7}+\cdots$
135.3.c.c	$135$	$3$	135.c	3.b	$2$	$4$	$4$	$3.678$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-12$		$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{3}q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots$
135.3.d.a	$135$	$3$	135.d	15.d	$2$	$2$	$2$	$3.678$	$\Q(\sqrt{-11}) $	$_{}$	None	None		$2$	$0$	$-2$	$0$	$-1$	$0$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-3q^{4}-\beta q^{5}+(-1+2\beta )q^{7}+\cdots$
135.3.d.b	$135$	$3$	135.d	15.d	$2$	$2$	$2$	$3.678$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$-2$	$0$	$8$	$0$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-3q^{4}+(4+i)q^{5}-2iq^{7}+7q^{8}+\cdots$
135.3.d.c	$135$	$3$	135.d	15.d	$2$	$2$	$2$	$3.678$	$\Q(\sqrt{5}) $	$_{}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$0$	$-1$	$0$	$10$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+(-1-\beta )q^{2}+(8+\beta )q^{4}+5q^{5}+(-15+\cdots)q^{8}+\cdots$
135.3.d.d	$135$	$3$	135.d	15.d	$2$	$2$	$2$	$3.678$	$\Q(\sqrt{5}) $	$_{}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$0$	$1$	$0$	$-10$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+(1+\beta )q^{2}+(8+\beta )q^{4}-5q^{5}+(15+\cdots)q^{8}+\cdots$
135.3.d.e	$135$	$3$	135.d	15.d	$2$	$2$	$2$	$3.678$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$2$	$0$	$-8$	$0$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-3q^{4}+(-4+i)q^{5}+2iq^{7}+\cdots$
135.3.d.f	$135$	$3$	135.d	15.d	$2$	$2$	$2$	$3.678$	$\Q(\sqrt{-11}) $	$_{}$	None	None		$2$	$0$	$2$	$0$	$1$	$0$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-3q^{4}+(1-\beta )q^{5}+(1-2\beta )q^{7}+\cdots$
135.3.d.g	$135$	$3$	135.d	15.d	$2$	$4$	$4$	$3.678$	$\Q(i, \sqrt{10})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+6q^{4}-\beta _{2}q^{5}+\beta _{1}q^{7}-2\beta _{3}q^{8}+\cdots$
135.3.g.a	$135$	$3$	135.g	5.c	$4$	$16$	$8$	$3.678$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-8$		$3^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+(2\beta _{4}+\beta _{7})q^{4}-\beta _{13}q^{5}+\cdots$
135.3.g.b	$135$	$3$	135.g	5.c	$4$	$16$	$8$	$3.678$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$16$		$2^{4}\cdot 3^{8}\cdot 5$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+(2\beta _{3}+\beta _{4})q^{4}+\beta _{10}q^{5}+\cdots$
135.3.h.a	$135$	$3$	135.h	45.h	$6$	$20$	$10$	$3.678$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$12$	$0$		$3^{12}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{2}q^{2}+(-2+\beta _{3}-2\beta _{5})q^{4}+(1+\cdots)q^{5}+\cdots$
135.3.i.a	$135$	$3$	135.i	9.d	$6$	$16$	$8$	$3.678$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$2$		$3^{6}$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{1}-\beta _{4})q^{2}+(\beta _{1}-\beta _{3}-\beta _{4}+2\beta _{7}+\cdots)q^{4}+\cdots$
135.3.l.a	$135$	$3$	135.l	45.k	$12$	$40$	$10$	$3.678$		$_{}$	None	None		$4$	$0$	$2$	$0$	$2$	$-2$			$\mathrm{SU}(2)[C_{12}]$
135.3.n.a	$135$	$3$	135.n	135.n	$18$	$204$	$34$	$3.678$		$_{}$	None	None		$4$	$0$	$0$	$0$	$3$	$0$			$\mathrm{SU}(2)[C_{18}]$
135.3.o.a	$135$	$3$	135.o	27.f	$18$	$144$	$24$	$3.678$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{18}]$
135.3.r.a	$135$	$3$	135.r	135.r	$36$	$408$	$34$	$3.678$		$_{}$	None	None		$4$	$0$	$-12$	$-12$	$-12$	$-12$			$\mathrm{SU}(2)[C_{36}]$
135.4.a.a	$135$	$4$	135.a	1.a	$1$	$1$	$1$	$7.965$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-2$	$0$	$5$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-4q^{4}+5q^{5}+24q^{8}-10q^{10}+\cdots$
135.4.a.b	$135$	$4$	135.a	1.a	$1$	$1$	$1$	$7.965$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$-5$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-7q^{4}-5q^{5}-6q^{7}+15q^{8}+\cdots$
135.4.a.c	$135$	$4$	135.a	1.a	$1$	$1$	$1$	$7.965$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$1$	$0$	$5$	$-6$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-7q^{4}+5q^{5}-6q^{7}-15q^{8}+\cdots$
135.4.a.d	$135$	$4$	135.a	1.a	$1$	$1$	$1$	$7.965$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$2$	$0$	$-5$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-4q^{4}-5q^{5}-24q^{8}-10q^{10}+\cdots$
135.4.a.e	$135$	$4$	135.a	1.a	$1$	$3$	$3$	$7.965$	3.3.1772.1	$_{}$	None	None	✓	$1$	$1$	$-5$	$0$	$-15$	$-4$	$-$	$3$	$\mathrm{SU}(2)$	$q+(-2+\beta _{1})q^{2}+(7-3\beta _{1}+\beta _{2})q^{4}+\cdots$
135.4.a.f	$135$	$4$	135.a	1.a	$1$	$3$	$3$	$7.965$	3.3.5637.1	$_{}$	None	None	✓	$1$	$0$	$-1$	$0$	$15$	$44$	$+$	$3$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(7+\beta _{1}+\beta _{2})q^{4}+5q^{5}+\cdots$
135.4.a.g	$135$	$4$	135.a	1.a	$1$	$3$	$3$	$7.965$	3.3.5637.1	$_{}$	None	None	✓	$1$	$0$	$1$	$0$	$-15$	$44$	$+$	$3$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(7+\beta _{1}+\beta _{2})q^{4}-5q^{5}+\cdots$
135.4.a.h	$135$	$4$	135.a	1.a	$1$	$3$	$3$	$7.965$	3.3.1772.1	$_{}$	None	None	✓	$1$	$0$	$5$	$0$	$15$	$-4$	$+$	$3$	$\mathrm{SU}(2)$	$q+(2-\beta _{1})q^{2}+(7-3\beta _{1}+\beta _{2})q^{4}+5q^{5}+\cdots$
135.4.b.a	$135$	$4$	135.b	5.b	$2$	$4$	$4$	$7.965$	$\Q(i, \sqrt{5})$	$_{}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$3^{4}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{2}+(-13-\beta _{3})q^{4}-5\beta _{1}q^{5}+\cdots$
135.4.b.b	$135$	$4$	135.b	5.b	$2$	$8$	$8$	$7.965$	8.0.$\cdots$.7	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+(1-\beta _{2})q^{4}+(\beta _{1}-\beta _{4}-2\beta _{5}+\cdots)q^{5}+\cdots$
135.4.b.c	$135$	$4$	135.b	5.b	$2$	$12$	$12$	$7.965$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 3^{18}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{2}+(-5-\beta _{1})q^{4}-\beta _{3}q^{5}+\beta _{8}q^{7}+\cdots$
135.4.e.a	$135$	$4$	135.e	9.c	$3$	$4$	$2$	$7.965$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		$2$	$0$	$-1$	$0$	$10$	$-9$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{3})q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots$
135.4.e.b	$135$	$4$	135.e	9.c	$3$	$6$	$3$	$7.965$	6.0.15759792.1	$_{}$	None	None		$2$	$0$	$-1$	$0$	$15$	$43$		$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{4})q^{2}+(-\beta _{2}+3\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots$
135.4.e.c	$135$	$4$	135.e	9.c	$3$	$14$	$7$	$7.965$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		$2$	$0$	$-2$	$0$	$-35$	$-22$		$2^{2}\cdot 3^{13}$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}-\beta _{2})q^{2}+(-5-\beta _{3}-5\beta _{5}-\beta _{10}+\cdots)q^{4}+\cdots$

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 199 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.