LMFDB - Newform search results

Refine search

Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

				Sort order	Select

Results (1-50 of 95 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	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
145.1.f.a	$145$	$1$	145.f	145.f	$4$	$2$	$1$	$0.072$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{5}) $		✓	✓	✓	145.1.f.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+i q^{4}-i q^{5}+i q^{9}+(-i-1)q^{11}+\cdots$
145.1.h.a	$145$	$1$	145.h	145.h	$4$	$2$	$1$	$0.072$	$\Q(\sqrt{-1}) $	$D_{4}$	None	$\Q(\sqrt{29}) $		✓	✓	✓	145.1.h.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$		$q-i q^{4}-i q^{5}+(i-1)q^{7}+i q^{9}+\cdots$
145.2.a.a	$145$	$2$	145.a	1.a	$1$	$1$	$1$	$1.158$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	145.2.a.a	$1$	$1$	$-1$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}-q^{5}-2q^{7}+3q^{8}-3q^{9}+\cdots$
145.2.a.b	$145$	$2$	145.a	1.a	$1$	$2$	$2$	$1.158$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	✓	✓	✓	145.2.a.b	$1$	$1$	$-2$	$-4$	$2$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-2q^{3}+(1-2\beta )q^{4}+\cdots$
145.2.a.c	$145$	$2$	145.a	1.a	$1$	$3$	$3$	$1.158$	3.3.148.1	$_{}$	None	None	✓	✓	✓	✓	145.2.a.c	$1$	$0$	$1$	$2$	$3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots$
145.2.a.d	$145$	$2$	145.a	1.a	$1$	$3$	$3$	$1.158$	3.3.148.1	$_{}$	None	None	✓	✓	✓	✓	145.2.a.d	$1$	$0$	$3$	$-2$	$-3$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta _{2})q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+\cdots$
145.2.b.a	$145$	$2$	145.b	5.b	$2$	$4$	$4$	$1.158$	$\Q(\sqrt{-3}, \sqrt{-11})$	$_{}$	None	None		✓			145.2.b.a	$2$	$0$	$0$	$0$	$-3$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{3})q^{3}-q^{4}+(-1+\cdots)q^{5}+\cdots$
145.2.b.b	$145$	$2$	145.b	5.b	$2$	$4$	$4$	$1.158$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		✓			145.2.b.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
145.2.b.c	$145$	$2$	145.b	5.b	$2$	$6$	$6$	$1.158$	6.0.84345856.2	$_{}$	None	None		✓	✓		145.2.b.c	$2$	$0$	$0$	$0$	$3$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{5})q^{3}+(-3+\beta _{3}+\cdots)q^{4}+\cdots$
145.2.c.a	$145$	$2$	145.c	29.b	$2$	$4$	$4$	$1.158$	$\Q(\sqrt{-2}, \sqrt{3})$	$_{}$	None	None		✓			145.2.c.a	$2$	$0$	$0$	$0$	$-4$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{4}-q^{5}+\cdots$
145.2.c.b	$145$	$2$	145.c	29.b	$2$	$6$	$6$	$1.158$	6.0.16516096.1	$_{}$	None	None		✓	✓		145.2.c.b	$2$	$0$	$0$	$0$	$6$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{5})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$
145.2.d.a	$145$	$2$	145.d	145.d	$2$	$4$	$4$	$1.158$	$\Q(\sqrt{-3}, \sqrt{17})$	$_{}$	None	None		✓			145.2.d.a	$2$	$0$	$-4$	$2$	$3$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-\beta _{2}q^{3}-q^{4}+(1+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
145.2.d.b	$145$	$2$	145.d	145.d	$2$	$4$	$4$	$1.158$	$\Q(i, \sqrt{5})$	$_{}$	None	None		✓			145.2.d.b	$4$	$0$	$0$	$0$	$-4$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+3q^{4}+(-1-\beta _{1})q^{5}+\beta _{1}q^{7}+\cdots$
145.2.d.c	$145$	$2$	145.d	145.d	$2$	$4$	$4$	$1.158$	$\Q(\sqrt{-3}, \sqrt{17})$	$_{}$	None	None		✓			145.2.d.a	$2$	$0$	$4$	$-2$	$3$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+(-1+\beta _{2})q^{3}-q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
145.2.e.a	$145$	$2$	145.e	145.e	$4$	$26$	$13$	$1.158$		$_{}$	None	None		✓	✓	✓	145.2.e.a	$2$	$0$	$0$	$-4$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
145.2.j.a	$145$	$2$	145.j	145.j	$4$	$26$	$13$	$1.158$		$_{}$	None	None		✓	✓	✓	145.2.e.a	$2$	$0$	$-6$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
145.2.k.a	$145$	$2$	145.k	29.d	$7$	$24$	$4$	$1.158$		$_{}$	None	None		✓			145.2.k.a	$2$	$0$	$-2$	$2$	$4$	$4$			$\mathrm{SU}(2)[C_{7}]$
145.2.k.b	$145$	$2$	145.k	29.d	$7$	$36$	$6$	$1.158$		$_{}$	None	None		✓	✓		145.2.k.b	$2$	$0$	$-2$	$-2$	$-6$	$-8$			$\mathrm{SU}(2)[C_{7}]$
145.2.l.a	$145$	$2$	145.l	145.l	$14$	$72$	$12$	$1.158$		$_{}$	None	None		✓	✓	✓	145.2.l.a	$4$	$0$	$0$	$0$	$-9$	$0$			$\mathrm{SU}(2)[C_{14}]$
145.2.m.a	$145$	$2$	145.m	29.e	$14$	$24$	$4$	$1.158$		$_{}$	None	None		✓			145.2.m.a	$2$	$0$	$0$	$0$	$4$	$4$			$\mathrm{SU}(2)[C_{14}]$
145.2.m.b	$145$	$2$	145.m	29.e	$14$	$36$	$6$	$1.158$		$_{}$	None	None		✓	✓		145.2.m.b	$2$	$0$	$0$	$0$	$-6$	$0$			$\mathrm{SU}(2)[C_{14}]$
145.2.n.a	$145$	$2$	145.n	145.n	$14$	$84$	$14$	$1.158$		$_{}$	None	None		✓	✓	✓	145.2.n.a	$4$	$0$	$0$	$0$	$-7$	$0$			$\mathrm{SU}(2)[C_{14}]$
145.2.o.a	$145$	$2$	145.o	145.o	$28$	$156$	$13$	$1.158$		$_{}$	None	None		✓	✓	✓	145.2.o.a	$2$	$0$	$-8$	$-14$	$-14$	$-10$			$\mathrm{SU}(2)[C_{28}]$
145.2.t.a	$145$	$2$	145.t	145.t	$28$	$156$	$13$	$1.158$		$_{}$	None	None		✓	✓	✓	145.2.o.a	$2$	$0$	$-14$	$-10$	$-14$	$-10$			$\mathrm{SU}(2)[C_{28}]$
145.3.f.a	$145$	$3$	145.f	145.f	$4$	$56$	$28$	$3.951$		$_{}$	None	None		✓	✓	✓	145.3.f.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
145.3.g.a	$145$	$3$	145.g	29.c	$4$	$40$	$20$	$3.951$		$_{}$	None	None		✓	✓	✓	145.3.g.a	$2$	$0$	$-4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
145.3.h.a	$145$	$3$	145.h	145.h	$4$	$56$	$28$	$3.951$		$_{}$	None	None		✓	✓	✓	145.3.h.a	$4$	$0$	$0$	$0$	$-12$	$-20$			$\mathrm{SU}(2)[C_{4}]$
145.3.i.a	$145$	$3$	145.i	5.c	$4$	$56$	$28$	$3.951$		$_{}$	None	None		✓	✓	✓	145.3.i.a	$2$	$0$	$0$	$-4$	$4$	$12$			$\mathrm{SU}(2)[C_{4}]$
145.3.p.a	$145$	$3$	145.p	145.p	$28$	$336$	$28$	$3.951$		$_{}$	None	None		✓	✓	✓	145.3.p.a	$4$	$0$	$-14$	$-10$	$-18$	$-26$			$\mathrm{SU}(2)[C_{28}]$
145.3.q.a	$145$	$3$	145.q	145.q	$28$	$336$	$28$	$3.951$		$_{}$	None	None		✓	✓	✓	145.3.q.a	$4$	$0$	$-14$	$-14$	$-2$	$6$			$\mathrm{SU}(2)[C_{28}]$
145.3.r.a	$145$	$3$	145.r	29.f	$28$	$240$	$20$	$3.951$		$_{}$	None	None		✓	✓	✓	145.3.r.a	$2$	$0$	$4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{28}]$
145.3.s.a	$145$	$3$	145.s	145.s	$28$	$336$	$28$	$3.951$		$_{}$	None	None		✓	✓	✓	145.3.s.a	$4$	$0$	$0$	$0$	$-14$	$0$			$\mathrm{SU}(2)[C_{28}]$
145.4.a.a	$145$	$4$	145.a	1.a	$1$	$1$	$1$	$8.555$	$\Q$	$_{}$	None	None	✓	✓			145.4.a.a	$1$	$0$	$1$	$-8$	$-5$	$-14$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-8q^{3}-7q^{4}-5q^{5}-8q^{6}+\cdots$
145.4.a.b	$145$	$4$	145.a	1.a	$1$	$6$	$6$	$8.555$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	145.4.a.b	$1$	$1$	$-7$	$-13$	$30$	$-79$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{2}+(-2+\beta _{1}+\beta _{4})q^{3}+\cdots$
145.4.a.c	$145$	$4$	145.a	1.a	$1$	$6$	$6$	$8.555$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	145.4.a.c	$1$	$1$	$-1$	$-1$	$-30$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-\beta _{3}-\beta _{4})q^{3}+(4+2\beta _{1}+\cdots)q^{4}+\cdots$
145.4.a.d	$145$	$4$	145.a	1.a	$1$	$7$	$7$	$8.555$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	$_{}$	None	None	✓	✓	✓		145.4.a.d	$1$	$0$	$6$	$1$	$-35$	$17$	$+$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	$q+(1-\beta _{4})q^{2}-\beta _{3}q^{3}+(8-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots$
145.4.a.e	$145$	$4$	145.a	1.a	$1$	$8$	$8$	$8.555$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	$_{}$	None	None	✓	✓	✓	✓	145.4.a.e	$1$	$0$	$5$	$17$	$40$	$33$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(2-\beta _{3})q^{3}+(5+\beta _{2}+\cdots)q^{4}+\cdots$
145.4.b.a	$145$	$4$	145.b	5.b	$2$	$18$	$18$	$8.555$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		✓			145.4.b.a	$2$	$0$	$0$	$0$	$-8$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{13}q^{3}+(-2+\beta _{2})q^{4}+\cdots$
145.4.b.b	$145$	$4$	145.b	5.b	$2$	$24$	$24$	$8.555$		$_{}$	None	None		✓	✓		145.4.b.b	$2$	$0$	$0$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{2}]$
145.4.c.a	$145$	$4$	145.c	29.b	$2$	$14$	$14$	$8.555$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		✓			145.4.c.a	$2$	$0$	$0$	$0$	$70$	$-10$		$2^{4}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-3+\beta _{2})q^{4}+5q^{5}+\cdots$
145.4.c.b	$145$	$4$	145.c	29.b	$2$	$16$	$16$	$8.555$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓	✓		145.4.c.b	$2$	$0$	$0$	$0$	$-80$	$38$		$2^{6}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{8}q^{3}+(-4+\beta _{2})q^{4}-5q^{5}+\cdots$
145.4.d.a	$145$	$4$	145.d	145.d	$2$	$44$	$44$	$8.555$		$_{}$	None	None		✓	✓	✓	145.4.d.a	$4$	$0$	$0$	$0$	$6$	$0$			$\mathrm{SU}(2)[C_{2}]$
145.4.e.a	$145$	$4$	145.e	145.e	$4$	$86$	$43$	$8.555$		$_{}$	None	None		✓	✓	✓	145.4.e.a	$2$	$0$	$0$	$-4$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
145.4.j.a	$145$	$4$	145.j	145.j	$4$	$86$	$43$	$8.555$		$_{}$	None	None		✓	✓	✓	145.4.e.a	$2$	$0$	$-8$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{4}]$
145.4.k.a	$145$	$4$	145.k	29.d	$7$	$84$	$14$	$8.555$		$_{}$	None	None		✓			145.4.k.a	$2$	$0$	$2$	$-4$	$-70$	$46$			$\mathrm{SU}(2)[C_{7}]$
145.4.k.b	$145$	$4$	145.k	29.d	$7$	$96$	$16$	$8.555$		$_{}$	None	None		✓	✓		145.4.k.b	$2$	$0$	$2$	$4$	$80$	$-18$			$\mathrm{SU}(2)[C_{7}]$
145.4.l.a	$145$	$4$	145.l	145.l	$14$	$264$	$44$	$8.555$		$_{}$	None	None		✓	✓	✓	145.4.l.a	$4$	$0$	$0$	$0$	$-13$	$0$			$\mathrm{SU}(2)[C_{14}]$
145.4.m.a	$145$	$4$	145.m	29.e	$14$	$84$	$14$	$8.555$		$_{}$	None	None		✓			145.4.m.a	$2$	$0$	$0$	$0$	$-70$	$10$			$\mathrm{SU}(2)[C_{14}]$
145.4.m.b	$145$	$4$	145.m	29.e	$14$	$96$	$16$	$8.555$		$_{}$	None	None		✓	✓		145.4.m.b	$2$	$0$	$0$	$0$	$80$	$-38$			$\mathrm{SU}(2)[C_{14}]$
145.4.n.a	$145$	$4$	145.n	145.n	$14$	$252$	$42$	$8.555$		$_{}$	None	None		✓	✓	✓	145.4.n.a	$4$	$0$	$0$	$0$	$9$	$0$			$\mathrm{SU}(2)[C_{14}]$

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 95 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.