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 119 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
2394.2.a.a	$2394$	$2$	2394.a	1.a	$1$	$1$	$1$	$19.116$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-4$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{5}+q^{7}-q^{8}+4q^{10}+\cdots$
2394.2.a.b	$2394$	$2$	2394.a	1.a	$1$	$1$	$1$	$19.116$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}+2q^{10}+\cdots$
2394.2.a.c	$2394$	$2$	2394.a	1.a	$1$	$1$	$1$	$19.116$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{7}-q^{8}-6q^{11}+2q^{13}+\cdots$
2394.2.a.d	$2394$	$2$	2394.a	1.a	$1$	$1$	$1$	$19.116$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{7}-q^{8}+2q^{13}-q^{14}+\cdots$
2394.2.a.e	$2394$	$2$	2394.a	1.a	$1$	$1$	$1$	$19.116$	$\Q$	None	✓	$1$	$1$	$-1$	$0$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-2q^{10}+\cdots$
2394.2.a.f	$2394$	$2$	2394.a	1.a	$1$	$1$	$1$	$19.116$	$\Q$	None	✓	$1$	$0$	$-1$	$0$	$4$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+4q^{5}-q^{7}-q^{8}-4q^{10}+\cdots$
2394.2.a.g	$2394$	$2$	2394.a	1.a	$1$	$1$	$1$	$19.116$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-4$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-4q^{5}+q^{7}+q^{8}-4q^{10}+\cdots$
2394.2.a.h	$2394$	$2$	2394.a	1.a	$1$	$1$	$1$	$19.116$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}-q^{7}+q^{8}-2q^{10}+\cdots$
2394.2.a.i	$2394$	$2$	2394.a	1.a	$1$	$1$	$1$	$19.116$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{7}+q^{8}-2q^{11}-4q^{13}+\cdots$
2394.2.a.j	$2394$	$2$	2394.a	1.a	$1$	$1$	$1$	$19.116$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{7}+q^{8}-6q^{11}-4q^{13}+\cdots$
2394.2.a.k	$2394$	$2$	2394.a	1.a	$1$	$1$	$1$	$19.116$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{13}+q^{14}+\cdots$
2394.2.a.l	$2394$	$2$	2394.a	1.a	$1$	$1$	$1$	$19.116$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{7}+q^{8}+6q^{11}+2q^{13}+\cdots$
2394.2.a.m	$2394$	$2$	2394.a	1.a	$1$	$1$	$1$	$19.116$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}+2q^{10}+\cdots$
2394.2.a.n	$2394$	$2$	2394.a	1.a	$1$	$1$	$1$	$19.116$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}+q^{7}+q^{8}+2q^{10}+\cdots$
2394.2.a.o	$2394$	$2$	2394.a	1.a	$1$	$1$	$1$	$19.116$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{5}+q^{7}+q^{8}+4q^{10}+\cdots$
2394.2.a.p	$2394$	$2$	2394.a	1.a	$1$	$2$	$2$	$19.116$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-2$	$0$	$-2$	$2$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1-\beta )q^{5}+q^{7}-q^{8}+\cdots$
2394.2.a.q	$2394$	$2$	2394.a	1.a	$1$	$2$	$2$	$19.116$	$\Q(\sqrt{13}) $	None	✓	$1$	$0$	$-2$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-\beta q^{5}+q^{7}-q^{8}+\beta q^{10}+\cdots$
2394.2.a.r	$2394$	$2$	2394.a	1.a	$1$	$2$	$2$	$19.116$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$-2$	$0$	$0$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+\beta q^{5}+q^{7}-q^{8}-\beta q^{10}+\cdots$
2394.2.a.s	$2394$	$2$	2394.a	1.a	$1$	$2$	$2$	$19.116$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$-2$	$0$	$2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(1+\beta )q^{5}-q^{7}-q^{8}+\cdots$
2394.2.a.t	$2394$	$2$	2394.a	1.a	$1$	$2$	$2$	$19.116$	$\Q(\sqrt{2}) $	None	✓	$1$	$0$	$-2$	$0$	$4$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots$
2394.2.a.u	$2394$	$2$	2394.a	1.a	$1$	$2$	$2$	$19.116$	$\Q(\sqrt{2}) $	None	✓	$1$	$1$	$2$	$0$	$-4$	$2$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}+q^{7}+q^{8}-2q^{10}+\cdots$
2394.2.a.v	$2394$	$2$	2394.a	1.a	$1$	$2$	$2$	$19.116$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$2$	$0$	$-2$	$-2$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(-1-\beta )q^{5}-q^{7}+q^{8}+\cdots$
2394.2.a.w	$2394$	$2$	2394.a	1.a	$1$	$2$	$2$	$19.116$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$2$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1-3\beta )q^{5}+q^{7}+q^{8}+\cdots$
2394.2.a.x	$2394$	$2$	2394.a	1.a	$1$	$2$	$2$	$19.116$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$0$	$0$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}-q^{7}+q^{8}+\beta q^{10}+\cdots$
2394.2.a.y	$2394$	$2$	2394.a	1.a	$1$	$2$	$2$	$19.116$	$\Q(\sqrt{29}) $	None	✓	$1$	$0$	$2$	$0$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta q^{5}-q^{7}+q^{8}+\beta q^{10}+\cdots$
2394.2.a.z	$2394$	$2$	2394.a	1.a	$1$	$2$	$2$	$19.116$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$2$	$0$	$2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1+\beta )q^{5}+q^{7}+q^{8}+\cdots$
2394.2.a.ba	$2394$	$2$	2394.a	1.a	$1$	$3$	$3$	$19.116$	3.3.469.1	None	✓	$1$	$0$	$-3$	$0$	$-5$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-2+\beta _{1})q^{5}-q^{7}-q^{8}+\cdots$
2394.2.a.bb	$2394$	$2$	2394.a	1.a	$1$	$3$	$3$	$19.116$	3.3.148.1	None	✓	$1$	$1$	$-3$	$0$	$-2$	$-3$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+(-1-\beta _{1})q^{5}-q^{7}-q^{8}+\cdots$
2394.2.a.bc	$2394$	$2$	2394.a	1.a	$1$	$3$	$3$	$19.116$	3.3.148.1	None	✓	$1$	$0$	$3$	$0$	$2$	$-3$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+(1+\beta _{1})q^{5}-q^{7}+q^{8}+\cdots$
2394.2.b.a	$2394$	$2$	2394.b	57.d	$2$	$2$	$2$	$19.116$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$-2$	$0$	$0$	$-2$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}-q^{7}-q^{8}-\beta q^{13}+q^{14}+\cdots$
2394.2.b.b	$2394$	$2$	2394.b	57.d	$2$	$2$	$2$	$19.116$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$-2$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+2\beta q^{5}+q^{7}-q^{8}-2\beta q^{10}+\cdots$
2394.2.b.c	$2394$	$2$	2394.b	57.d	$2$	$2$	$2$	$19.116$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$-2$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+\beta q^{5}+q^{7}-q^{8}-\beta q^{10}+\cdots$
2394.2.b.d	$2394$	$2$	2394.b	57.d	$2$	$2$	$2$	$19.116$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$2$	$0$	$0$	$-2$		$3$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}-q^{7}+q^{8}-\beta q^{13}-q^{14}+\cdots$
2394.2.b.e	$2394$	$2$	2394.b	57.d	$2$	$2$	$2$	$19.116$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$2$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+2\beta q^{5}+q^{7}+q^{8}+2\beta q^{10}+\cdots$
2394.2.b.f	$2394$	$2$	2394.b	57.d	$2$	$2$	$2$	$19.116$	$\Q(\sqrt{-2}) $	None		$2$	$0$	$2$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+\beta q^{5}+q^{7}+q^{8}+\beta q^{10}+\cdots$
2394.2.b.g	$2394$	$2$	2394.b	57.d	$2$	$6$	$6$	$19.116$	6.0.2803712.1	None		$2$	$0$	$-6$	$0$	$0$	$6$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}-\beta _{1}q^{5}+q^{7}-q^{8}+\beta _{1}q^{10}+\cdots$
2394.2.b.h	$2394$	$2$	2394.b	57.d	$2$	$6$	$6$	$19.116$	6.0.2803712.1	None		$2$	$0$	$6$	$0$	$0$	$6$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}-\beta _{1}q^{5}+q^{7}+q^{8}-\beta _{1}q^{10}+\cdots$
2394.2.b.i	$2394$	$2$	2394.b	57.d	$2$	$8$	$8$	$19.116$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$-8$	$0$	$0$	$-8$		$2^{5}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}+\beta _{3}q^{5}-q^{7}-q^{8}-\beta _{3}q^{10}+\cdots$
2394.2.b.j	$2394$	$2$	2394.b	57.d	$2$	$8$	$8$	$19.116$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$8$	$0$	$0$	$-8$		$2^{5}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}+\beta _{3}q^{5}-q^{7}+q^{8}+\beta _{3}q^{10}+\cdots$
2394.2.e.a	$2394$	$2$	2394.e	133.c	$2$	$12$	$12$	$19.116$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}-q^{4}-\beta _{2}q^{5}+\beta _{7}q^{7}-\beta _{4}q^{8}+\cdots$
2394.2.e.b	$2394$	$2$	2394.e	133.c	$2$	$12$	$12$	$19.116$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}-q^{4}-\beta _{2}q^{5}+\beta _{7}q^{7}+\beta _{4}q^{8}+\cdots$
2394.2.e.c	$2394$	$2$	2394.e	133.c	$2$	$16$	$16$	$19.116$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$6$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{11}q^{2}-q^{4}-\beta _{7}q^{5}+\beta _{12}q^{7}+\cdots$
2394.2.e.d	$2394$	$2$	2394.e	133.c	$2$	$24$	$24$	$19.116$		None		$8$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{2}]$
2394.2.f.a	$2394$	$2$	2394.f	21.c	$2$	$24$	$24$	$19.116$		None		$2$	$0$	$0$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{2}]$
2394.2.f.b	$2394$	$2$	2394.f	21.c	$2$	$24$	$24$	$19.116$		None		$2$	$0$	$0$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{2}]$
2394.2.o.a	$2394$	$2$	2394.o	19.c	$3$	$2$	$1$	$19.116$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$-3$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{5}+\cdots$
2394.2.o.b	$2394$	$2$	2394.o	19.c	$3$	$2$	$1$	$19.116$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$-3$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{5}+\cdots$
2394.2.o.c	$2394$	$2$	2394.o	19.c	$3$	$2$	$1$	$19.116$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$-1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots$
2394.2.o.d	$2394$	$2$	2394.o	19.c	$3$	$2$	$1$	$19.116$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots$
2394.2.o.e	$2394$	$2$	2394.o	19.c	$3$	$2$	$1$	$19.116$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots$

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 119 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.