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 (45 matches)

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
471.1.d.a	$471$	$1$	471.d	471.d	$2$	$1$	$1$	$0.235$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-471}) $	$\Q(\sqrt{157}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$		$1$		$q+q^{3}-q^{4}+q^{9}-q^{12}+2q^{13}+q^{16}+\cdots$
471.1.d.b	$471$	$1$	471.d	471.d	$2$	$2$	$2$	$0.235$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-471}) $	None	✓	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q-\beta q^{2}+q^{3}+q^{4}+\beta q^{5}-\beta q^{6}+q^{9}+\cdots$
471.1.d.c	$471$	$1$	471.d	471.d	$2$	$4$	$4$	$0.235$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-471}) $	None	✓	$4$	$0$	$0$	$-4$	$0$	$0$		$1$		$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots$
471.1.n.a	$471$	$1$	471.n	471.n	$26$	$12$	$1$	$0.235$	$\Q(\zeta_{26})$	$D_{26}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$0$		$1$		$q+\zeta_{26}^{2}q^{3}+\zeta_{26}^{11}q^{4}+(\zeta_{26}^{5}+\zeta_{26}^{12}+\cdots)q^{7}+\cdots$
471.1.o.a	$471$	$1$	471.o	471.o	$26$	$12$	$1$	$0.235$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$		$1$		$q-\zeta_{26}^{3}q^{3}+\zeta_{26}^{10}q^{4}+(-\zeta_{26}-\zeta_{26}^{5}+\cdots)q^{7}+\cdots$
471.2.a.a	$471$	$2$	471.a	1.a	$1$	$1$	$1$	$3.761$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-1$	$-2$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+3q^{7}+\cdots$
471.2.a.b	$471$	$2$	471.a	1.a	$1$	$2$	$2$	$3.761$	$\Q(\sqrt{5}) $	$_{}$	None	None	✓	$1$	$1$	$-1$	$2$	$-2$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots$
471.2.a.c	$471$	$2$	471.a	1.a	$1$	$3$	$3$	$3.761$	3.3.229.1	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
471.2.a.d	$471$	$2$	471.a	1.a	$1$	$9$	$9$	$3.761$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$2$	$-9$	$8$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{5}+\cdots)q^{5}+\cdots$
471.2.a.e	$471$	$2$	471.a	1.a	$1$	$12$	$12$	$3.761$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$-1$	$12$	$4$	$8$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{8}q^{5}+\cdots$
471.2.b.a	$471$	$2$	471.b	157.b	$2$	$12$	$12$	$3.761$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-12$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-q^{3}+(-1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
471.2.b.b	$471$	$2$	471.b	157.b	$2$	$14$	$14$	$3.761$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$14$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+q^{3}+(-1+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots$
471.2.e.a	$471$	$2$	471.e	157.c	$3$	$4$	$2$	$3.761$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$2$	$0$	$0$	$2$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}+(1+\beta _{2})q^{3}-2\beta _{1}q^{5}-\beta _{1}q^{6}+\cdots$
471.2.e.b	$471$	$2$	471.e	157.c	$3$	$22$	$11$	$3.761$		$_{}$	None	None		$2$	$0$	$2$	$11$	$-4$	$4$			$\mathrm{SU}(2)[C_{3}]$
471.2.e.c	$471$	$2$	471.e	157.c	$3$	$28$	$14$	$3.761$		$_{}$	None	None		$2$	$0$	$2$	$-14$	$-2$	$4$			$\mathrm{SU}(2)[C_{3}]$
471.2.f.a	$471$	$2$	471.f	471.f	$4$	$100$	$50$	$3.761$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-12$			$\mathrm{SU}(2)[C_{4}]$
471.2.h.a	$471$	$2$	471.h	157.e	$6$	$24$	$12$	$3.761$		$_{}$	None	None		$2$	$0$	$0$	$12$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
471.2.h.b	$471$	$2$	471.h	157.e	$6$	$26$	$13$	$3.761$		$_{}$	None	None		$2$	$0$	$0$	$-13$	$-6$	$0$			$\mathrm{SU}(2)[C_{6}]$
471.2.l.a	$471$	$2$	471.l	471.l	$12$	$4$	$1$	$3.761$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$6$	$0$	$-8$		$1$	$\mathrm{U}(1)[D_{12}]$	$q+(2-\zeta_{12}^{2})q^{3}-2\zeta_{12}^{3}q^{4}+(-3+\cdots)q^{7}+\cdots$
471.2.l.b	$471$	$2$	471.l	471.l	$12$	$200$	$50$	$3.761$		$_{}$	None	None		$4$	$0$	$0$	$-6$	$0$	$0$			$\mathrm{SU}(2)[C_{12}]$
471.2.m.a	$471$	$2$	471.m	157.g	$13$	$156$	$13$	$3.761$		$_{}$	None	None		$2$	$0$	$-1$	$13$	$-4$	$2$			$\mathrm{SU}(2)[C_{13}]$
471.2.m.b	$471$	$2$	471.m	157.g	$13$	$180$	$15$	$3.761$		$_{}$	None	None		$2$	$0$	$-1$	$-15$	$-8$	$-10$			$\mathrm{SU}(2)[C_{13}]$
471.2.p.a	$471$	$2$	471.p	157.h	$26$	$144$	$12$	$3.761$		$_{}$	None	None		$2$	$0$	$0$	$12$	$0$	$0$			$\mathrm{SU}(2)[C_{26}]$
471.2.p.b	$471$	$2$	471.p	157.h	$26$	$168$	$14$	$3.761$		$_{}$	None	None		$2$	$0$	$0$	$-14$	$0$	$0$			$\mathrm{SU}(2)[C_{26}]$
471.2.q.a	$471$	$2$	471.q	157.i	$39$	$312$	$13$	$3.761$		$_{}$	None	None		$2$	$0$	$-2$	$-13$	$4$	$4$			$\mathrm{SU}(2)[C_{39}]$
471.2.q.b	$471$	$2$	471.q	157.i	$39$	$336$	$14$	$3.761$		$_{}$	None	None		$2$	$0$	$-2$	$14$	$2$	$-4$			$\mathrm{SU}(2)[C_{39}]$
471.2.s.a	$471$	$2$	471.s	471.s	$52$	$1200$	$50$	$3.761$		$_{}$	None	None		$4$	$0$	$0$	$-26$	$0$	$-40$			$\mathrm{SU}(2)[C_{52}]$
471.2.v.a	$471$	$2$	471.v	157.k	$78$	$288$	$12$	$3.761$		$_{}$	None	None		$2$	$0$	$0$	$-12$	$0$	$0$			$\mathrm{SU}(2)[C_{78}]$
471.2.v.b	$471$	$2$	471.v	157.k	$78$	$312$	$13$	$3.761$		$_{}$	None	None		$2$	$0$	$0$	$13$	$6$	$0$			$\mathrm{SU}(2)[C_{78}]$
471.2.w.a	$471$	$2$	471.w	471.w	$156$	$48$	$1$	$3.761$		$_{}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-6$	$0$	$8$			$\mathrm{U}(1)[D_{156}]$
471.2.w.b	$471$	$2$	471.w	471.w	$156$	$2400$	$50$	$3.761$		$_{}$	None	None		$4$	$0$	$0$	$-46$	$0$	$-104$			$\mathrm{SU}(2)[C_{156}]$
471.4.a.a	$471$	$4$	471.a	1.a	$1$	$14$	$14$	$27.790$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-2$	$42$	$-32$	$-60$	$-$	$2^{6}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+3q^{3}+(2+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots$
471.4.a.b	$471$	$4$	471.a	1.a	$1$	$17$	$17$	$27.790$	$\mathbb{Q}[x]/(x^{17} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-2$	$-51$	$-28$	$10$	$-$	$2^{3}\cdot 5$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}-3q^{3}+(4+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots$
471.4.a.c	$471$	$4$	471.a	1.a	$1$	$22$	$22$	$27.790$		$_{}$	None	None	✓	$1$	$0$	$4$	$-66$	$32$	$-4$	$+$		$\mathrm{SU}(2)$
471.4.a.d	$471$	$4$	471.a	1.a	$1$	$25$	$25$	$27.790$		$_{}$	None	None	✓	$1$	$0$	$4$	$75$	$28$	$94$	$+$		$\mathrm{SU}(2)$
471.4.b.a	$471$	$4$	471.b	157.b	$2$	$40$	$40$	$27.790$		$_{}$	None	None		$2$	$0$	$0$	$-120$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
471.4.b.b	$471$	$4$	471.b	157.b	$2$	$40$	$40$	$27.790$		$_{}$	None	None		$2$	$0$	$0$	$120$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
471.6.a.a	$471$	$6$	471.a	1.a	$1$	$27$	$27$	$75.541$		$_{}$	None	None	✓	$1$	$1$	$-2$	$243$	$-164$	$-618$	$+$		$\mathrm{SU}(2)$
471.6.a.b	$471$	$6$	471.a	1.a	$1$	$30$	$30$	$75.541$		$_{}$	None	None	✓	$1$	$1$	$-8$	$-270$	$-136$	$68$	$+$		$\mathrm{SU}(2)$
471.6.a.c	$471$	$6$	471.a	1.a	$1$	$35$	$35$	$75.541$		$_{}$	None	None	✓	$1$	$0$	$4$	$-315$	$164$	$-30$	$-$		$\mathrm{SU}(2)$
471.6.a.d	$471$	$6$	471.a	1.a	$1$	$38$	$38$	$75.541$		$_{}$	None	None	✓	$1$	$0$	$10$	$342$	$136$	$460$	$-$		$\mathrm{SU}(2)$
471.8.a.a	$471$	$8$	471.a	1.a	$1$	$40$	$40$	$147.133$		$_{}$	None	None	✓	$1$	$1$	$-16$	$1080$	$-428$	$-3424$	$-$		$\mathrm{SU}(2)$
471.8.a.b	$471$	$8$	471.a	1.a	$1$	$43$	$43$	$147.133$		$_{}$	None	None	✓	$1$	$1$	$-22$	$-1161$	$-1072$	$6$	$-$		$\mathrm{SU}(2)$
471.8.a.c	$471$	$8$	471.a	1.a	$1$	$48$	$48$	$147.133$		$_{}$	None	None	✓	$1$	$0$	$2$	$-1296$	$428$	$-680$	$+$		$\mathrm{SU}(2)$
471.8.a.d	$471$	$8$	471.a	1.a	$1$	$51$	$51$	$147.133$		$_{}$	None	None	✓	$1$	$0$	$8$	$1377$	$1072$	$4122$	$+$		$\mathrm{SU}(2)$

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 (45 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.