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 109 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
1472.1.f.a	$1472$	$1$	1472.f	23.b	$2$	$1$	$1$	$0.735$	$\Q$	$D_{3}$	$\Q(\sqrt{-23}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$0$		$1$		$q-q^{3}+q^{13}-q^{23}+q^{25}+q^{27}+\cdots$
1472.1.f.b	$1472$	$1$	1472.f	23.b	$2$	$1$	$1$	$0.735$	$\Q$	$D_{3}$	$\Q(\sqrt{-23}) $	None	✓	$2$	$0$	$0$	$1$	$0$	$0$		$1$		$q+q^{3}+q^{13}+q^{23}+q^{25}-q^{27}+\cdots$
1472.1.k.a	$1472$	$1$	1472.k	368.k	$4$	$2$	$1$	$0.735$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$		$1$		$q+(-1-i)q^{3}+iq^{9}+(-1-i)q^{13}+\cdots$
1472.1.k.b	$1472$	$1$	1472.k	368.k	$4$	$4$	$2$	$0.735$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$2$	$0$	$0$		$2$		$q+(-\zeta_{12}+\zeta_{12}^{2})q^{3}+(\zeta_{12}^{2}-\zeta_{12}^{3}+\cdots)q^{9}+\cdots$
1472.1.s.a	$1472$	$1$	1472.s	1472.s	$16$	$8$	$1$	$0.735$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{16}q^{2}+(\zeta_{16}-\zeta_{16}^{4})q^{3}+\zeta_{16}^{2}q^{4}+\cdots$
1472.1.s.b	$1472$	$1$	1472.s	1472.s	$16$	$16$	$2$	$0.735$	$\Q(\zeta_{48})$	$D_{48}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{48}q^{2}+(-\zeta_{48}^{4}+\zeta_{48}^{17})q^{3}+\cdots$
1472.2.a.a	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-2q^{7}+6q^{9}+5q^{13}-6q^{17}+\cdots$
1472.2.a.b	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+2q^{5}+4q^{7}+6q^{9}+2q^{11}+\cdots$
1472.2.a.c	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$0$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{7}-2q^{9}+q^{13}-6q^{17}+\cdots$
1472.2.a.d	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$2$	$4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+2q^{5}+4q^{7}-2q^{9}-2q^{11}+\cdots$
1472.2.a.e	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-1$	$4$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+4q^{5}-2q^{7}-2q^{9}-4q^{11}+\cdots$
1472.2.a.f	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}-4q^{7}-3q^{9}-2q^{11}+2q^{13}+\cdots$
1472.2.a.g	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+4q^{7}-3q^{9}+2q^{11}+2q^{13}+\cdots$
1472.2.a.h	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{7}-3q^{9}+6q^{11}+2q^{13}+6q^{17}+\cdots$
1472.2.a.i	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{7}-3q^{9}-6q^{11}+2q^{13}+6q^{17}+\cdots$
1472.2.a.j	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-2q^{7}-2q^{9}+q^{13}-6q^{17}+\cdots$
1472.2.a.k	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+2q^{5}-4q^{7}-2q^{9}+2q^{11}+\cdots$
1472.2.a.l	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$4$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+4q^{5}+2q^{7}-2q^{9}+4q^{11}+\cdots$
1472.2.a.m	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+2q^{7}+6q^{9}+5q^{13}-6q^{17}+\cdots$
1472.2.a.n	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$2$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}+2q^{5}-4q^{7}+6q^{9}-2q^{11}+\cdots$
1472.2.a.o	$1472$	$2$	1472.a	1.a	$1$	$2$	$2$	$11.754$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$4$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{3}+(2-\beta )q^{5}+(-2+\beta )q^{7}+\cdots$
1472.2.a.p	$1472$	$2$	1472.a	1.a	$1$	$2$	$2$	$11.754$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-1$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{3}-2q^{5}+(1+\beta )q^{9}+2\beta q^{11}+\cdots$
1472.2.a.q	$1472$	$2$	1472.a	1.a	$1$	$2$	$2$	$11.754$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-2$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1-\beta )q^{5}+(-3+\beta )q^{7}+\cdots$
1472.2.a.r	$1472$	$2$	1472.a	1.a	$1$	$2$	$2$	$11.754$	$\Q(\sqrt{3}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-2$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}+(-1+\beta )q^{5}+(3+\beta )q^{7}+(-3+\cdots)q^{11}+\cdots$
1472.2.a.s	$1472$	$2$	1472.a	1.a	$1$	$2$	$2$	$11.754$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$-2$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1-\beta )q^{5}+(-1-\beta )q^{7}+2q^{9}+\cdots$
1472.2.a.t	$1472$	$2$	1472.a	1.a	$1$	$2$	$2$	$11.754$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(1+\beta )q^{5}+(1-\beta )q^{7}+2q^{9}+\cdots$
1472.2.a.u	$1472$	$2$	1472.a	1.a	$1$	$2$	$2$	$11.754$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$1$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{3}-2q^{5}+(1+\beta )q^{9}-2\beta q^{11}+\cdots$
1472.2.a.v	$1472$	$2$	1472.a	1.a	$1$	$2$	$2$	$11.754$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{3}+(2+\beta )q^{5}+(2+\beta )q^{7}+\cdots$
1472.2.a.w	$1472$	$2$	1472.a	1.a	$1$	$3$	$3$	$11.754$	3.3.316.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-4$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots$
1472.2.a.x	$1472$	$2$	1472.a	1.a	$1$	$3$	$3$	$11.754$	3.3.316.1	$_{}$	None	None	✓	$1$	$0$	$0$	$4$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+(1+\cdots)q^{7}+\cdots$
1472.2.a.y	$1472$	$2$	1472.a	1.a	$1$	$4$	$4$	$11.754$	4.4.13768.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$-6$	$-4$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{2}q^{3}+(-2+\beta _{3})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
1472.2.a.z	$1472$	$2$	1472.a	1.a	$1$	$4$	$4$	$11.754$	4.4.13768.1	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-6$	$4$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{2}q^{3}+(-2+\beta _{3})q^{5}+(1-\beta _{1})q^{7}+\cdots$
1472.2.b.a	$1472$	$2$	1472.b	8.b	$2$	$6$	$6$	$11.754$	6.0.399424.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-4$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+(-\beta _{3}-\beta _{5})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
1472.2.b.b	$1472$	$2$	1472.b	8.b	$2$	$6$	$6$	$11.754$	6.0.399424.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$4$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+(\beta _{3}+\beta _{5})q^{5}+(1-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
1472.2.b.c	$1472$	$2$	1472.b	8.b	$2$	$16$	$16$	$11.754$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-4$		$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{11}q^{5}-\beta _{9}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots$
1472.2.b.d	$1472$	$2$	1472.b	8.b	$2$	$16$	$16$	$11.754$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$4$		$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{11}q^{5}+\beta _{9}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots$
1472.2.c.a	$1472$	$2$	1472.c	92.b	$2$	$4$	$4$	$11.754$	$\Q(\sqrt{2}, \sqrt{-5})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}-2q^{9}+3\beta _{1}q^{11}+\cdots$
1472.2.c.b	$1472$	$2$	1472.c	92.b	$2$	$4$	$4$	$11.754$	$\Q(i, \sqrt{14})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{2}q^{5}-\beta _{3}q^{7}+2q^{9}-\beta _{3}q^{11}+\cdots$
1472.2.c.c	$1472$	$2$	1472.c	92.b	$2$	$6$	$6$	$11.754$	6.0.8869743.1	$_{}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{7}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{3}+(-3-\beta _{2})q^{9}+(-\beta _{2}-\beta _{4}+\cdots)q^{13}+\cdots$
1472.2.c.d	$1472$	$2$	1472.c	92.b	$2$	$8$	$8$	$11.754$	8.0.303595776.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+\beta _{4}q^{5}-\beta _{6}q^{7}+\beta _{7}q^{9}+\cdots$
1472.2.c.e	$1472$	$2$	1472.c	92.b	$2$	$24$	$24$	$11.754$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1472.2.h.a	$1472$	$2$	1472.h	184.h	$2$	$8$	$8$	$11.754$	8.0.$\cdots$.3	$_{}$	$\Q(\sqrt{-46}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{3}q^{5}-3q^{9}-\beta _{4}q^{11}+\beta _{7}q^{19}+\cdots$
1472.2.h.b	$1472$	$2$	1472.h	184.h	$2$	$8$	$8$	$11.754$	8.0.157351936.1	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{3}+\beta _{3}q^{5}+\beta _{7}q^{7}+4q^{9}-\beta _{5}q^{11}+\cdots$
1472.2.h.c	$1472$	$2$	1472.h	184.h	$2$	$32$	$32$	$11.754$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1472.2.i.a	$1472$	$2$	1472.i	368.i	$4$	$12$	$6$	$11.754$	12.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{U}(1)[D_{4}]$	$q+\beta _{3}q^{3}+(-3\beta _{1}-\beta _{3}+\beta _{4}+\beta _{11})q^{9}+\cdots$
1472.2.i.b	$1472$	$2$	1472.i	368.i	$4$	$80$	$40$	$11.754$		$_{}$	None	None		$4$	$0$	$0$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
1472.2.j.a	$1472$	$2$	1472.j	16.e	$4$	$2$	$1$	$11.754$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$1$	$0$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+i)q^{3}+4iq^{7}+iq^{9}+(-4+\cdots)q^{11}+\cdots$
1472.2.j.b	$1472$	$2$	1472.j	16.e	$4$	$4$	$2$	$11.754$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$6$	$-4$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+(-1-\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
1472.2.j.c	$1472$	$2$	1472.j	16.e	$4$	$12$	$6$	$11.754$	12.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$-2$	$-4$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{3}+(-1+\beta _{2}+\beta _{3}+\beta _{5}-\beta _{6}+\cdots)q^{5}+\cdots$
1472.2.j.d	$1472$	$2$	1472.j	16.e	$4$	$24$	$12$	$11.754$		$_{}$	None	None		$2$	$0$	$0$	$4$	$4$	$0$			$\mathrm{SU}(2)[C_{4}]$

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 109 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.