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 142 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
520.1.b.a	$520$	$1$	520.b	520.b	$2$	$2$	$2$	$0.260$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-10}) $, $\Q(\sqrt{-26}) $	$\Q(\sqrt{65}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{2}-q^{4}+iq^{5}-iq^{7}+iq^{8}+\cdots$
520.1.b.b	$520$	$1$	520.b	520.b	$2$	$4$	$4$	$0.260$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-26}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{3}q^{2}+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{3}+\cdots$
520.1.bg.a	$520$	$1$	520.bg	520.ag	$4$	$4$	$2$	$0.260$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{26}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}q^{5}-\zeta_{8}^{3}q^{8}+\cdots$
520.1.bo.a	$520$	$1$	520.bo	520.ao	$4$	$4$	$2$	$0.260$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{10}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}^{3}q^{2}+(-\zeta_{8}+\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots$
520.1.bx.a	$520$	$1$	520.bx	520.ax	$6$	$2$	$1$	$0.260$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$-1$	$0$	$2$	$1$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+q^{5}-\zeta_{6}^{2}q^{7}+\cdots$
520.1.bx.b	$520$	$1$	520.bx	520.ax	$6$	$2$	$1$	$0.260$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$1$	$0$	$-2$	$-1$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{5}+\zeta_{6}^{2}q^{7}+\cdots$
520.1.cd.a	$520$	$1$	520.cd	520.bd	$6$	$4$	$2$	$0.260$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-10}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{3}q^{5}+\cdots$
520.2.a.a	$520$	$2$	520.a	1.a	$1$	$1$	$1$	$4.152$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{9}-4q^{11}-q^{13}-6q^{17}+\cdots$
520.2.a.b	$520$	$2$	520.a	1.a	$1$	$1$	$1$	$4.152$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+q^{9}+2q^{11}+q^{13}+\cdots$
520.2.a.c	$520$	$2$	520.a	1.a	$1$	$2$	$2$	$4.152$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-4$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-2+\beta )q^{3}+q^{5}-2q^{7}+(3-4\beta )q^{9}+\cdots$
520.2.a.d	$520$	$2$	520.a	1.a	$1$	$2$	$2$	$4.152$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}-q^{5}-2\beta q^{7}+(1-2\beta )q^{9}+\cdots$
520.2.a.e	$520$	$2$	520.a	1.a	$1$	$2$	$2$	$4.152$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}-q^{5}+2\beta q^{7}+(1-2\beta )q^{9}+\cdots$
520.2.a.f	$520$	$2$	520.a	1.a	$1$	$2$	$2$	$4.152$	$\Q(\sqrt{6}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+q^{5}+2q^{7}+3q^{9}+(-2+\beta )q^{11}+\cdots$
520.2.a.g	$520$	$2$	520.a	1.a	$1$	$2$	$2$	$4.152$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}-q^{5}+(3+2\beta )q^{9}+(3-\beta )q^{11}+\cdots$
520.2.d.a	$520$	$2$	520.d	5.b	$2$	$2$	$2$	$4.152$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(2+i)q^{5}-4iq^{7}+3q^{9}-2q^{11}+\cdots$
520.2.d.b	$520$	$2$	520.d	5.b	$2$	$6$	$6$	$4.152$	6.0.350464.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{3}+\beta _{4})q^{3}+(\beta _{1}+\beta _{4})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots$
520.2.d.c	$520$	$2$	520.d	5.b	$2$	$10$	$10$	$4.152$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{9}q^{3}-\beta _{1}q^{5}-\beta _{4}q^{7}+(-4-\beta _{5}+\cdots)q^{9}+\cdots$
520.2.e.a	$520$	$2$	520.e	104.e	$2$	$28$	$28$	$4.152$		$_{}$	None	None		$2$	$0$	$0$	$0$	$-28$	$0$			$\mathrm{SU}(2)[C_{2}]$
520.2.e.b	$520$	$2$	520.e	104.e	$2$	$28$	$28$	$4.152$		$_{}$	None	None		$2$	$0$	$0$	$0$	$28$	$0$			$\mathrm{SU}(2)[C_{2}]$
520.2.f.a	$520$	$2$	520.f	65.d	$2$	$10$	$10$	$4.152$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-3$	$2$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+\beta _{6}q^{5}-\beta _{2}q^{7}+(-1-\beta _{1}+\cdots)q^{9}+\cdots$
520.2.f.b	$520$	$2$	520.f	65.d	$2$	$10$	$10$	$4.152$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$3$	$-2$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}-\beta _{6}q^{5}+\beta _{2}q^{7}+(-1-\beta _{1}+\cdots)q^{9}+\cdots$
520.2.g.a	$520$	$2$	520.g	8.b	$2$	$24$	$24$	$4.152$		$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$-16$			$\mathrm{SU}(2)[C_{2}]$
520.2.g.b	$520$	$2$	520.g	8.b	$2$	$24$	$24$	$4.152$		$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$24$			$\mathrm{SU}(2)[C_{2}]$
520.2.j.a	$520$	$2$	520.j	40.f	$2$	$36$	$36$	$4.152$		$_{}$	None	None		$2$	$0$	$0$	$-8$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
520.2.j.b	$520$	$2$	520.j	40.f	$2$	$36$	$36$	$4.152$		$_{}$	None	None		$2$	$0$	$0$	$8$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
520.2.k.a	$520$	$2$	520.k	13.b	$2$	$6$	$6$	$4.152$	6.0.350464.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}-\beta _{3}q^{5}+(\beta _{3}-\beta _{4}+\beta _{5})q^{7}+\cdots$
520.2.k.b	$520$	$2$	520.k	13.b	$2$	$8$	$8$	$4.152$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$4$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}-\beta _{2}q^{5}+(\beta _{2}+\beta _{4}-\beta _{5})q^{7}+\cdots$
520.2.p.a	$520$	$2$	520.p	520.p	$2$	$8$	$8$	$4.152$	8.0.207360000.1	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-\beta _{4}+\beta _{7})q^{3}-\beta _{5}q^{4}+\cdots$
520.2.p.b	$520$	$2$	520.p	520.p	$2$	$72$	$72$	$4.152$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
520.2.q.a	$520$	$2$	520.q	13.c	$3$	$2$	$1$	$4.152$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$-2$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{3}-q^{5}-3\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
520.2.q.b	$520$	$2$	520.q	13.c	$3$	$2$	$1$	$4.152$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$-2$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}-q^{5}+3\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots$
520.2.q.c	$520$	$2$	520.q	13.c	$3$	$2$	$1$	$4.152$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$-2$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}-q^{5}+3\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots$
520.2.q.d	$520$	$2$	520.q	13.c	$3$	$2$	$1$	$4.152$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$2$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{3}+q^{5}+3\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots$
520.2.q.e	$520$	$2$	520.q	13.c	$3$	$2$	$1$	$4.152$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$3$	$-2$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(3-3\zeta_{6})q^{3}-q^{5}-3\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots$
520.2.q.f	$520$	$2$	520.q	13.c	$3$	$4$	$2$	$4.152$	$\Q(\sqrt{-3}, \sqrt{17})$	$_{}$	None	None		$2$	$0$	$0$	$1$	$4$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{3}+q^{5}+(-1+\beta _{2})q^{7}+(-1+\cdots)q^{9}+\cdots$
520.2.q.g	$520$	$2$	520.q	13.c	$3$	$6$	$3$	$4.152$	6.0.27870912.1	$_{}$	None	None		$2$	$0$	$0$	$-1$	$-6$	$-9$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{3}-q^{5}+(-3+3\beta _{4})q^{7}+(-1+\cdots)q^{9}+\cdots$
520.2.q.h	$520$	$2$	520.q	13.c	$3$	$8$	$4$	$4.152$	8.0.649638144.4	$_{}$	None	None		$2$	$0$	$0$	$0$	$8$	$4$		$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{3}+q^{5}+(1+\beta _{3}+\beta _{4}-\beta _{5}+\cdots)q^{7}+\cdots$
520.2.t.a	$520$	$2$	520.t	520.t	$4$	$4$	$2$	$4.152$	$\Q(i, \sqrt{10})$	$_{}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$-4$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-1-\beta _{2})q^{2}+2\beta _{2}q^{4}+\beta _{1}q^{5}+\cdots$
520.2.t.b	$520$	$2$	520.t	520.t	$4$	$4$	$2$	$4.152$	$\Q(i, \sqrt{10})$	$_{}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(1-\beta _{2})q^{2}-2\beta _{2}q^{4}-\beta _{3}q^{5}+2\beta _{1}q^{7}+\cdots$
520.2.t.c	$520$	$2$	520.t	520.t	$4$	$152$	$76$	$4.152$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
520.2.w.a	$520$	$2$	520.w	65.k	$4$	$2$	$1$	$4.152$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$1$	$0$	$-2$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-i)q^{3}+(-2-i)q^{5}-iq^{9}+\cdots$
520.2.w.b	$520$	$2$	520.w	65.k	$4$	$2$	$1$	$4.152$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2-i)q^{5}+4iq^{7}-3iq^{9}+(4+\cdots)q^{11}+\cdots$
520.2.w.c	$520$	$2$	520.w	65.k	$4$	$2$	$1$	$4.152$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+i)q^{3}+(1-2i)q^{5}-2iq^{7}-iq^{9}+\cdots$
520.2.w.d	$520$	$2$	520.w	65.k	$4$	$4$	$2$	$4.152$	$\Q(\zeta_{8})$	$_{}$	None	None		$2$	$0$	$0$	$-4$	$-4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\zeta_{8}-\zeta_{8}^{2})q^{3}+(-1+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots$
520.2.w.e	$520$	$2$	520.w	65.k	$4$	$12$	$6$	$4.152$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$4$	$8$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{3}+(1-\beta _{7})q^{5}-\beta _{10}q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots$
520.2.w.f	$520$	$2$	520.w	65.k	$4$	$20$	$10$	$4.152$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-2$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{3}q^{3}+\beta _{7}q^{5}-\beta _{11}q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots$
520.2.y.a	$520$	$2$	520.y	520.y	$4$	$160$	$80$	$4.152$		$_{}$	None	None		$4$	$0$	$-4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
520.2.bc.a	$520$	$2$	520.bc	520.ac	$4$	$12$	$6$	$4.152$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	$\Q(\sqrt{-26}) $	None		$4$	$0$	$-12$	$0$	$0$	$0$		$5$	$\mathrm{U}(1)[D_{4}]$	$q+(-1-\beta _{4})q^{2}+\beta _{3}q^{3}+2\beta _{4}q^{4}+\cdots$
520.2.bc.b	$520$	$2$	520.bc	520.ac	$4$	$12$	$6$	$4.152$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	$\Q(\sqrt{-26}) $	None		$4$	$0$	$12$	$0$	$0$	$0$		$5$	$\mathrm{U}(1)[D_{4}]$	$q+(1-\beta _{3})q^{2}-\beta _{10}q^{3}-2\beta _{3}q^{4}-\beta _{9}q^{5}+\cdots$
520.2.bc.c	$520$	$2$	520.bc	520.ac	$4$	$136$	$68$	$4.152$		$_{}$	None	None		$8$	$0$	$0$	$-8$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$

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 142 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.