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 80 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
215.1.d.a	$215$	$1$	215.d	215.d	$2$	$3$	$3$	$0.107$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-215}) $	None	✓	$2$	$0$	$-1$	$-1$	$3$	$-1$		$1$		$q-\beta _{1}q^{2}+\beta _{2}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots$
215.1.d.b	$215$	$1$	215.d	215.d	$2$	$3$	$3$	$0.107$	$\Q(\zeta_{14})^+$	$D_{7}$	$\Q(\sqrt{-215}) $	None	✓	$2$	$0$	$1$	$1$	$-3$	$1$		$1$		$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
215.2.a.a	$215$	$2$	215.a	1.a	$1$	$1$	$1$	$1.717$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{5}-2q^{7}-3q^{9}-q^{11}+\cdots$
215.2.a.b	$215$	$2$	215.a	1.a	$1$	$3$	$3$	$1.717$	3.3.321.1	$_{}$	None	None	✓	$1$	$0$	$-2$	$1$	$3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+\beta _{1}q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots$
215.2.a.c	$215$	$2$	215.a	1.a	$1$	$5$	$5$	$1.717$	5.5.1933097.1	$_{}$	None	None	✓	$1$	$0$	$2$	$-1$	$5$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(2+\beta _{2}+\cdots)q^{4}+\cdots$
215.2.a.d	$215$	$2$	215.a	1.a	$1$	$6$	$6$	$1.717$	6.6.32503921.1	$_{}$	None	None	✓	$1$	$0$	$3$	$4$	$-6$	$8$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-\beta _{3})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots$
215.2.b.a	$215$	$2$	215.b	5.b	$2$	$6$	$6$	$1.717$	6.0.1827904.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$-12$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{4}-\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots$
215.2.b.b	$215$	$2$	215.b	5.b	$2$	$14$	$14$	$1.717$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$8$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{9})q^{2}+(-\beta _{9}-\beta _{13})q^{3}+(-1+\cdots)q^{4}+\cdots$
215.2.e.a	$215$	$2$	215.e	43.c	$3$	$2$	$1$	$1.717$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$2$	$-1$	$-1$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+q^{2}+(-1+\zeta_{6})q^{3}-q^{4}+(-1+\zeta_{6})q^{5}+\cdots$
215.2.e.b	$215$	$2$	215.e	43.c	$3$	$4$	$2$	$1.717$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		$2$	$0$	$2$	$-3$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}+(1-\beta _{1}+2\beta _{2}-\beta _{3})q^{3}+\cdots$
215.2.e.c	$215$	$2$	215.e	43.c	$3$	$10$	$5$	$1.717$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		$2$	$0$	$-4$	$1$	$-5$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{7})q^{2}+(1-\beta _{1}-\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots$
215.2.e.d	$215$	$2$	215.e	43.c	$3$	$12$	$6$	$1.717$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-3$	$6$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{6}q^{2}-\beta _{10}q^{3}+(1+\beta _{3})q^{4}+(1+\cdots)q^{5}+\cdots$
215.2.g.a	$215$	$2$	215.g	215.g	$4$	$40$	$20$	$1.717$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
215.2.i.a	$215$	$2$	215.i	215.i	$6$	$40$	$20$	$1.717$		$_{}$	None	None		$4$	$0$	$0$	$0$	$1$	$0$			$\mathrm{SU}(2)[C_{6}]$
215.2.k.a	$215$	$2$	215.k	43.e	$7$	$42$	$7$	$1.717$		$_{}$	None	None		$2$	$0$	$-3$	$-4$	$7$	$8$			$\mathrm{SU}(2)[C_{7}]$
215.2.k.b	$215$	$2$	215.k	43.e	$7$	$54$	$9$	$1.717$		$_{}$	None	None		$2$	$0$	$-3$	$-4$	$-9$	$4$			$\mathrm{SU}(2)[C_{7}]$
215.2.l.a	$215$	$2$	215.l	215.l	$12$	$4$	$1$	$1.717$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$-2$	$2$	$2$	$-2$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots$
215.2.l.b	$215$	$2$	215.l	215.l	$12$	$4$	$1$	$1.717$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$2$	$4$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(1+\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(1+\cdots)q^{3}+\cdots$
215.2.l.c	$215$	$2$	215.l	215.l	$12$	$72$	$18$	$1.717$		$_{}$	None	None		$4$	$0$	$0$	$-12$	$-6$	$-12$			$\mathrm{SU}(2)[C_{12}]$
215.2.p.a	$215$	$2$	215.p	215.p	$14$	$120$	$20$	$1.717$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-3$	$0$			$\mathrm{SU}(2)[C_{14}]$
215.2.q.a	$215$	$2$	215.q	43.g	$21$	$72$	$6$	$1.717$		$_{}$	None	None		$2$	$0$	$0$	$3$	$-6$	$-10$			$\mathrm{SU}(2)[C_{21}]$
215.2.q.b	$215$	$2$	215.q	43.g	$21$	$96$	$8$	$1.717$		$_{}$	None	None		$2$	$0$	$0$	$3$	$8$	$-12$			$\mathrm{SU}(2)[C_{21}]$
215.2.r.a	$215$	$2$	215.r	215.r	$28$	$240$	$20$	$1.717$		$_{}$	None	None		$4$	$0$	$-14$	$-14$	$-14$	$0$			$\mathrm{SU}(2)[C_{28}]$
215.2.u.a	$215$	$2$	215.u	215.u	$42$	$240$	$20$	$1.717$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-15$	$0$			$\mathrm{SU}(2)[C_{42}]$
215.2.x.a	$215$	$2$	215.x	215.x	$84$	$480$	$20$	$1.717$		$_{}$	None	None		$4$	$0$	$-28$	$-22$	$-22$	$-30$			$\mathrm{SU}(2)[C_{84}]$
215.3.c.a	$215$	$3$	215.c	43.b	$2$	$2$	$2$	$5.858$	$\Q(\sqrt{-5}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-2\beta q^{3}-q^{4}-\beta q^{5}+10q^{6}+\cdots$
215.3.c.b	$215$	$3$	215.c	43.b	$2$	$26$	$26$	$5.858$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
215.3.d.a	$215$	$3$	215.d	215.d	$2$	$7$	$7$	$5.858$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	$\Q(\sqrt{-215}) $	None	✓	$2$	$0$	$0$	$0$	$-35$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(4+\beta _{2}+\beta _{4})q^{4}+\cdots$
215.3.d.b	$215$	$3$	215.d	215.d	$2$	$7$	$7$	$5.858$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	$\Q(\sqrt{-215}) $	None	✓	$2$	$0$	$0$	$0$	$35$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{2}-\beta _{4}q^{3}+(4+\beta _{2}+\beta _{4})q^{4}+\cdots$
215.3.d.c	$215$	$3$	215.d	215.d	$2$	$28$	$28$	$5.858$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
215.3.f.a	$215$	$3$	215.f	5.c	$4$	$84$	$42$	$5.858$		$_{}$	None	None		$2$	$0$	$-4$	$-4$	$-8$	$-16$			$\mathrm{SU}(2)[C_{4}]$
215.3.h.a	$215$	$3$	215.h	43.d	$6$	$60$	$30$	$5.858$		$_{}$	None	None		$2$	$0$	$0$	$-6$	$0$	$-42$			$\mathrm{SU}(2)[C_{6}]$
215.3.j.a	$215$	$3$	215.j	215.j	$6$	$84$	$42$	$5.858$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-3$	$0$			$\mathrm{SU}(2)[C_{6}]$
215.3.m.a	$215$	$3$	215.m	215.m	$12$	$168$	$42$	$5.858$		$_{}$	None	None		$4$	$0$	$-8$	$-2$	$2$	$-8$			$\mathrm{SU}(2)[C_{12}]$
215.3.n.a	$215$	$3$	215.n	215.n	$14$	$252$	$42$	$5.858$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-7$	$0$			$\mathrm{SU}(2)[C_{14}]$
215.3.o.a	$215$	$3$	215.o	43.f	$14$	$168$	$28$	$5.858$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{14}]$
215.3.s.a	$215$	$3$	215.s	215.s	$28$	$504$	$42$	$5.858$		$_{}$	None	None		$4$	$0$	$-10$	$-10$	$-6$	$-12$			$\mathrm{SU}(2)[C_{28}]$
215.3.t.a	$215$	$3$	215.t	215.t	$42$	$504$	$42$	$5.858$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-11$	$0$			$\mathrm{SU}(2)[C_{42}]$
215.3.v.a	$215$	$3$	215.v	43.h	$42$	$360$	$30$	$5.858$		$_{}$	None	None		$2$	$0$	$0$	$6$	$0$	$42$			$\mathrm{SU}(2)[C_{42}]$
215.3.w.a	$215$	$3$	215.w	215.w	$84$	$1008$	$42$	$5.858$		$_{}$	None	None		$4$	$0$	$-20$	$-26$	$-30$	$-6$			$\mathrm{SU}(2)[C_{84}]$
215.4.a.a	$215$	$4$	215.a	1.a	$1$	$6$	$6$	$12.685$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-5$	$-5$	$30$	$-34$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(-1-\beta _{5})q^{3}+(1+\cdots)q^{4}+\cdots$
215.4.a.b	$215$	$4$	215.a	1.a	$1$	$8$	$8$	$12.685$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	$1$	$1$	$-1$	$-7$	$-40$	$-36$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(3+\beta _{2})q^{4}+\cdots$
215.4.a.c	$215$	$4$	215.a	1.a	$1$	$13$	$13$	$12.685$	$\mathbb{Q}[x]/(x^{13} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$5$	$5$	$-65$	$34$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(5+\beta _{2})q^{4}-5q^{5}+\cdots$
215.4.a.d	$215$	$4$	215.a	1.a	$1$	$15$	$15$	$12.685$	$\mathbb{Q}[x]/(x^{15} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$1$	$7$	$75$	$36$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{5}q^{3}+(6+\beta _{2})q^{4}+5q^{5}+\cdots$
215.4.b.a	$215$	$4$	215.b	5.b	$2$	$64$	$64$	$12.685$		$_{}$	None	None		$2$	$0$	$0$	$0$	$6$	$0$			$\mathrm{SU}(2)[C_{2}]$
215.4.e.a	$215$	$4$	215.e	43.c	$3$	$42$	$21$	$12.685$		$_{}$	None	None		$2$	$0$	$-2$	$4$	$-105$	$46$			$\mathrm{SU}(2)[C_{3}]$
215.4.e.b	$215$	$4$	215.e	43.c	$3$	$46$	$23$	$12.685$		$_{}$	None	None		$2$	$0$	$-2$	$4$	$115$	$50$			$\mathrm{SU}(2)[C_{3}]$
215.4.g.a	$215$	$4$	215.g	215.g	$4$	$128$	$64$	$12.685$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
215.4.i.a	$215$	$4$	215.i	215.i	$6$	$128$	$64$	$12.685$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-9$	$0$			$\mathrm{SU}(2)[C_{6}]$
215.4.k.a	$215$	$4$	215.k	43.e	$7$	$126$	$21$	$12.685$		$_{}$	None	None		$2$	$0$	$4$	$-2$	$-105$	$-100$			$\mathrm{SU}(2)[C_{7}]$

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 80 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.