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 60 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
2574.2.a.a	$2574$	$2$	2574.a	1.a	$1$	$1$	$1$	$20.553$	$\Q$	None	✓	$1$	$2$	$-1$	$0$	$-4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{5}-4q^{7}-q^{8}+4q^{10}+\cdots$
2574.2.a.b	$2574$	$2$	2574.a	1.a	$1$	$1$	$1$	$20.553$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{5}-q^{8}+4q^{10}-q^{11}+\cdots$
2574.2.a.c	$2574$	$2$	2574.a	1.a	$1$	$1$	$1$	$20.553$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-2q^{7}-q^{8}+2q^{10}+\cdots$
2574.2.a.d	$2574$	$2$	2574.a	1.a	$1$	$1$	$1$	$20.553$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}+4q^{7}-q^{8}+2q^{10}+\cdots$
2574.2.a.e	$2574$	$2$	2574.a	1.a	$1$	$1$	$1$	$20.553$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}+4q^{7}-q^{8}+2q^{10}+\cdots$
2574.2.a.f	$2574$	$2$	2574.a	1.a	$1$	$1$	$1$	$20.553$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-3q^{7}-q^{8}+q^{10}+\cdots$
2574.2.a.g	$2574$	$2$	2574.a	1.a	$1$	$1$	$1$	$20.553$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}+3q^{7}-q^{8}+q^{10}+\cdots$
2574.2.a.h	$2574$	$2$	2574.a	1.a	$1$	$1$	$1$	$20.553$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{7}-q^{8}+q^{11}+q^{13}+\cdots$
2574.2.a.i	$2574$	$2$	2574.a	1.a	$1$	$1$	$1$	$20.553$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}-3q^{7}-q^{8}-q^{10}+\cdots$
2574.2.a.j	$2574$	$2$	2574.a	1.a	$1$	$1$	$1$	$20.553$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots$
2574.2.a.k	$2574$	$2$	2574.a	1.a	$1$	$1$	$1$	$20.553$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots$
2574.2.a.l	$2574$	$2$	2574.a	1.a	$1$	$1$	$1$	$20.553$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-2q^{7}-q^{8}-2q^{10}+\cdots$
2574.2.a.m	$2574$	$2$	2574.a	1.a	$1$	$1$	$1$	$20.553$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-q^{8}-2q^{10}-q^{11}+\cdots$
2574.2.a.n	$2574$	$2$	2574.a	1.a	$1$	$1$	$1$	$20.553$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$3$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{5}-5q^{7}-q^{8}-3q^{10}+\cdots$
2574.2.a.o	$2574$	$2$	2574.a	1.a	$1$	$1$	$1$	$20.553$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$3$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{5}+q^{7}-q^{8}-3q^{10}+\cdots$
2574.2.a.p	$2574$	$2$	2574.a	1.a	$1$	$1$	$1$	$20.553$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$3$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{5}+5q^{7}-q^{8}-3q^{10}+\cdots$
2574.2.a.q	$2574$	$2$	2574.a	1.a	$1$	$1$	$1$	$20.553$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$-3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{5}-q^{7}+q^{8}-3q^{10}+\cdots$
2574.2.a.r	$2574$	$2$	2574.a	1.a	$1$	$1$	$1$	$20.553$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-3q^{5}-q^{7}+q^{8}-3q^{10}+\cdots$
2574.2.a.s	$2574$	$2$	2574.a	1.a	$1$	$1$	$1$	$20.553$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}-2q^{7}+q^{8}-2q^{10}+\cdots$
2574.2.a.t	$2574$	$2$	2574.a	1.a	$1$	$1$	$1$	$20.553$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}-q^{11}+\cdots$
2574.2.a.u	$2574$	$2$	2574.a	1.a	$1$	$1$	$1$	$20.553$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-4q^{7}+q^{8}+q^{11}+q^{13}+\cdots$
2574.2.a.v	$2574$	$2$	2574.a	1.a	$1$	$1$	$1$	$20.553$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{7}+q^{8}-q^{11}+q^{13}+\cdots$
2574.2.a.w	$2574$	$2$	2574.a	1.a	$1$	$1$	$1$	$20.553$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots$
2574.2.a.x	$2574$	$2$	2574.a	1.a	$1$	$1$	$1$	$20.553$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}-2q^{7}+q^{8}+2q^{10}+\cdots$
2574.2.a.y	$2574$	$2$	2574.a	1.a	$1$	$1$	$1$	$20.553$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}+4q^{7}+q^{8}+2q^{10}+\cdots$
2574.2.a.z	$2574$	$2$	2574.a	1.a	$1$	$2$	$2$	$20.553$	$\Q(\sqrt{41}) $	None	✓	$1$	$0$	$-2$	$0$	$-4$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}+q^{11}+\cdots$
2574.2.a.ba	$2574$	$2$	2574.a	1.a	$1$	$2$	$2$	$20.553$	$\Q(\sqrt{15}) $	None	✓	$1$	$0$	$-2$	$0$	$-2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-q^{5}-\beta q^{7}-q^{8}+q^{10}+\cdots$
2574.2.a.bb	$2574$	$2$	2574.a	1.a	$1$	$2$	$2$	$20.553$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$-2$	$0$	$0$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}+2q^{7}-q^{8}-\beta q^{10}+\cdots$
2574.2.a.bc	$2574$	$2$	2574.a	1.a	$1$	$2$	$2$	$20.553$	$\Q(\sqrt{33}) $	None	✓	$1$	$0$	$2$	$0$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-\beta q^{5}-\beta q^{7}+q^{8}-\beta q^{10}+\cdots$
2574.2.a.bd	$2574$	$2$	2574.a	1.a	$1$	$2$	$2$	$20.553$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$0$	$0$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}+2q^{7}+q^{8}+\beta q^{10}+\cdots$
2574.2.a.be	$2574$	$2$	2574.a	1.a	$1$	$2$	$2$	$20.553$	$\Q(\sqrt{41}) $	None	✓	$1$	$0$	$2$	$0$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}+(2-\beta )q^{7}+q^{8}+\cdots$
2574.2.a.bf	$2574$	$2$	2574.a	1.a	$1$	$2$	$2$	$20.553$	$\Q(\sqrt{15}) $	None	✓	$1$	$0$	$2$	$0$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}-\beta q^{7}+q^{8}+q^{10}+\cdots$
2574.2.a.bg	$2574$	$2$	2574.a	1.a	$1$	$2$	$2$	$20.553$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$2$	$0$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1+\beta )q^{5}+(-1+\beta )q^{7}+\cdots$
2574.2.a.bh	$2574$	$2$	2574.a	1.a	$1$	$3$	$3$	$20.553$	3.3.316.1	None	✓	$1$	$0$	$-3$	$0$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(2\beta _{1}-\beta _{2})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
2574.2.a.bi	$2574$	$2$	2574.a	1.a	$1$	$3$	$3$	$20.553$	3.3.961.1	None	✓	$1$	$1$	$3$	$0$	$-2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1+\beta _{1})q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
2574.2.a.bj	$2574$	$2$	2574.a	1.a	$1$	$3$	$3$	$20.553$	3.3.316.1	None	✓	$1$	$0$	$3$	$0$	$-2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-2\beta _{1}+\beta _{2})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
2574.2.b.a	$2574$	$2$	2574.b	33.d	$2$	$4$	$4$	$20.553$	$\Q(\zeta_{8})$	None		$2$	$0$	$-4$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+2\zeta_{8}q^{5}+(2\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{7}+\cdots$
2574.2.b.b	$2574$	$2$	2574.b	33.d	$2$	$4$	$4$	$20.553$	$\Q(\zeta_{8})$	None		$2$	$0$	$4$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+2\zeta_{8}q^{5}+(-2\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{7}+\cdots$
2574.2.b.c	$2574$	$2$	2574.b	33.d	$2$	$20$	$20$	$20.553$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$-20$	$0$	$0$	$0$		$2^{12}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}-\beta _{7}q^{5}+(\beta _{10}+\beta _{11})q^{7}+\cdots$
2574.2.b.d	$2574$	$2$	2574.b	33.d	$2$	$20$	$20$	$20.553$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$20$	$0$	$0$	$0$		$2^{12}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}-\beta _{7}q^{5}+(-\beta _{10}-\beta _{11}+\cdots)q^{7}+\cdots$
2574.2.c.a	$2574$	$2$	2574.c	13.b	$2$	$2$	$2$	$20.553$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-q^{4}+3iq^{5}-iq^{7}-iq^{8}+\cdots$
2574.2.c.b	$2574$	$2$	2574.c	13.b	$2$	$2$	$2$	$20.553$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-q^{4}+iq^{5}+iq^{7}-iq^{8}+\cdots$
2574.2.c.c	$2574$	$2$	2574.c	13.b	$2$	$2$	$2$	$20.553$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}-q^{4}+iq^{8}-iq^{11}+(2-3i)q^{13}+\cdots$
2574.2.c.d	$2574$	$2$	2574.c	13.b	$2$	$2$	$2$	$20.553$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}-q^{4}+iq^{5}+iq^{7}+iq^{8}+\cdots$
2574.2.c.e	$2574$	$2$	2574.c	13.b	$2$	$2$	$2$	$20.553$	$\Q(\sqrt{-1}) $	None		$2$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-iq^{2}-q^{4}+2iq^{5}-4iq^{7}+iq^{8}+\cdots$
2574.2.c.f	$2574$	$2$	2574.c	13.b	$2$	$4$	$4$	$20.553$	$\Q(\zeta_{12})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{12}q^{2}-q^{4}+3\zeta_{12}q^{5}-\zeta_{12}^{2}q^{7}+\cdots$
2574.2.c.g	$2574$	$2$	2574.c	13.b	$2$	$4$	$4$	$20.553$	$\Q(i, \sqrt{17})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-q^{4}-\beta _{2}q^{5}+(-2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
2574.2.c.h	$2574$	$2$	2574.c	13.b	$2$	$4$	$4$	$20.553$	$\Q(i, \sqrt{41})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}-q^{4}+\beta _{1}q^{5}-\beta _{1}q^{7}-\beta _{2}q^{8}+\cdots$
2574.2.c.i	$2574$	$2$	2574.c	13.b	$2$	$8$	$8$	$20.553$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}-\beta _{2}q^{7}+\beta _{1}q^{8}+\cdots$
2574.2.c.j	$2574$	$2$	2574.c	13.b	$2$	$8$	$8$	$20.553$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-q^{4}+\beta _{3}q^{5}-\beta _{2}q^{7}+\beta _{1}q^{8}+\cdots$

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 60 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.