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 114 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
174.2.a.a	$174$	$2$	174.a	1.a	$1$	$1$	$1$	$1.389$	$\Q$	None	✓	$1$	$0$	$-1$	$-1$	$3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}-3q^{7}+\cdots$
174.2.a.b	$174$	$2$	174.a	1.a	$1$	$1$	$1$	$1.389$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$-3$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}+5q^{7}+\cdots$
174.2.a.c	$174$	$2$	174.a	1.a	$1$	$1$	$1$	$1.389$	$\Q$	None	✓	$1$	$0$	$-1$	$1$	$2$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots$
174.2.a.d	$174$	$2$	174.a	1.a	$1$	$1$	$1$	$1.389$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
174.2.a.e	$174$	$2$	174.a	1.a	$1$	$1$	$1$	$1.389$	$\Q$	None	✓	$1$	$0$	$1$	$1$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots$
174.2.d.a	$174$	$2$	174.d	29.b	$2$	$2$	$2$	$1.389$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$0$	$2$	$6$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}-iq^{3}-q^{4}+q^{5}+q^{6}+3q^{7}+\cdots$
174.2.d.b	$174$	$2$	174.d	29.b	$2$	$4$	$4$	$1.389$	$\Q(i, \sqrt{33})$	None		$2$	$0$	$0$	$0$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+\beta _{2}q^{3}-q^{4}+(-1+\beta _{3})q^{5}+\cdots$
174.2.f.a	$174$	$2$	174.f	87.f	$4$	$4$	$2$	$1.389$	$\Q(\zeta_{8})$	None		$4$	$0$	$0$	$-4$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+(-1+\zeta_{8}+\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
174.2.f.b	$174$	$2$	174.f	87.f	$4$	$4$	$2$	$1.389$	$\Q(\zeta_{8})$	None		$2$	$0$	$0$	$-4$	$4$	$-12$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
174.2.f.c	$174$	$2$	174.f	87.f	$4$	$4$	$2$	$1.389$	$\Q(\zeta_{8})$	None		$2$	$0$	$0$	$4$	$-4$	$-12$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{8}q^{2}+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots$
174.2.f.d	$174$	$2$	174.f	87.f	$4$	$8$	$4$	$1.389$	$\Q(\zeta_{24})$	None		$4$	$0$	$0$	$4$	$0$	$16$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{24}^{3}q^{2}+(1-\zeta_{24}^{2}-\zeta_{24}^{3}-\zeta_{24}^{4}+\cdots)q^{3}+\cdots$
174.2.g.a	$174$	$2$	174.g	29.d	$7$	$6$	$1$	$1.389$	$\Q(\zeta_{14})$	None		$2$	$0$	$-1$	$1$	$-1$	$6$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+\zeta_{14}^{4}q^{2}+(1-\zeta_{14}+\zeta_{14}^{2}-\zeta_{14}^{3}+\cdots)q^{3}+\cdots$
174.2.g.b	$174$	$2$	174.g	29.d	$7$	$6$	$1$	$1.389$	$\Q(\zeta_{14})$	None		$2$	$0$	$1$	$1$	$4$	$-4$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q-\zeta_{14}^{4}q^{2}+(1-\zeta_{14}+\zeta_{14}^{2}-\zeta_{14}^{3}+\cdots)q^{3}+\cdots$
174.2.g.c	$174$	$2$	174.g	29.d	$7$	$12$	$2$	$1.389$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$2$	$-2$	$1$	$2$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+\beta _{8}q^{2}+\beta _{6}q^{3}+\beta _{4}q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$
174.2.h.a	$174$	$2$	174.h	29.e	$14$	$12$	$2$	$1.389$	$\Q(\zeta_{28})$	None		$2$	$0$	$0$	$0$	$-2$	$8$		$1$	$\mathrm{SU}(2)[C_{14}]$	$q-\zeta_{28}^{9}q^{2}-\zeta_{28}^{3}q^{3}-\zeta_{28}^{4}q^{4}+\cdots$
174.2.h.b	$174$	$2$	174.h	29.e	$14$	$24$	$4$	$1.389$		None		$2$	$0$	$0$	$0$	$2$	$-12$			$\mathrm{SU}(2)[C_{14}]$
174.2.k.a	$174$	$2$	174.k	87.k	$28$	$120$	$10$	$1.389$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{28}]$
174.3.b.a	$174$	$3$	174.b	3.b	$2$	$20$	$20$	$4.741$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$8$		$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+\beta _{1}q^{3}-2q^{4}-\beta _{15}q^{5}+\cdots$
174.3.c.a	$174$	$3$	174.c	87.d	$2$	$20$	$20$	$4.741$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$-8$		$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-\beta _{14}q^{3}+2q^{4}+\beta _{6}q^{5}+\cdots$
174.3.e.a	$174$	$3$	174.e	29.c	$4$	$4$	$2$	$4.741$	$\Q(i, \sqrt{6})$	None		$2$	$0$	$-4$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{2})q^{2}+\beta _{1}q^{3}+2\beta _{2}q^{4}+\cdots$
174.3.e.b	$174$	$3$	174.e	29.c	$4$	$4$	$2$	$4.741$	$\Q(i, \sqrt{6})$	None		$2$	$0$	$-4$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{2})q^{2}+\beta _{1}q^{3}+2\beta _{2}q^{4}+\cdots$
174.3.e.c	$174$	$3$	174.e	29.c	$4$	$4$	$2$	$4.741$	$\Q(i, \sqrt{6})$	None		$2$	$0$	$4$	$0$	$0$	$44$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{2})q^{2}+\beta _{1}q^{3}+2\beta _{2}q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots$
174.3.e.d	$174$	$3$	174.e	29.c	$4$	$8$	$4$	$4.741$	8.0.$\cdots$.31	None		$2$	$0$	$8$	$0$	$0$	$-36$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\beta _{2})q^{2}-\beta _{4}q^{3}-2\beta _{2}q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots$
174.3.i.a	$174$	$3$	174.i	87.h	$14$	$120$	$20$	$4.741$		None		$4$	$0$	$0$	$0$	$0$	$8$			$\mathrm{SU}(2)[C_{14}]$
174.3.j.a	$174$	$3$	174.j	87.j	$14$	$120$	$20$	$4.741$		None		$4$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{14}]$
174.3.l.a	$174$	$3$	174.l	29.f	$28$	$48$	$4$	$4.741$		None		$2$	$0$	$8$	$0$	$28$	$8$			$\mathrm{SU}(2)[C_{28}]$
174.3.l.b	$174$	$3$	174.l	29.f	$28$	$72$	$6$	$4.741$		None		$2$	$0$	$-12$	$0$	$-28$	$-8$			$\mathrm{SU}(2)[C_{28}]$
174.4.a.a	$174$	$4$	174.a	1.a	$1$	$1$	$1$	$10.266$	$\Q$	None	✓	$1$	$0$	$-2$	$-3$	$-14$	$-21$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}-14q^{5}+6q^{6}+\cdots$
174.4.a.b	$174$	$4$	174.a	1.a	$1$	$1$	$1$	$10.266$	$\Q$	None	✓	$1$	$1$	$-2$	$-3$	$-8$	$19$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}-8q^{5}+6q^{6}+\cdots$
174.4.a.c	$174$	$4$	174.a	1.a	$1$	$1$	$1$	$10.266$	$\Q$	None	✓	$1$	$0$	$-2$	$-3$	$21$	$19$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-3q^{3}+4q^{4}+21q^{5}+6q^{6}+\cdots$
174.4.a.d	$174$	$4$	174.a	1.a	$1$	$1$	$1$	$10.266$	$\Q$	None	✓	$1$	$1$	$-2$	$3$	$0$	$-17$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}-6q^{6}-17q^{7}+\cdots$
174.4.a.e	$174$	$4$	174.a	1.a	$1$	$1$	$1$	$10.266$	$\Q$	None	✓	$1$	$1$	$2$	$-3$	$-10$	$7$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}-10q^{5}-6q^{6}+\cdots$
174.4.a.f	$174$	$4$	174.a	1.a	$1$	$1$	$1$	$10.266$	$\Q$	None	✓	$1$	$1$	$2$	$3$	$-18$	$-29$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}-18q^{5}+6q^{6}+\cdots$
174.4.a.g	$174$	$4$	174.a	1.a	$1$	$2$	$2$	$10.266$	$\Q(\sqrt{457}) $	None	✓	$1$	$0$	$4$	$-6$	$-5$	$14$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}-3q^{3}+4q^{4}+(-2-\beta )q^{5}+\cdots$
174.4.a.h	$174$	$4$	174.a	1.a	$1$	$3$	$3$	$10.266$	3.3.973681.1	None	✓	$1$	$0$	$-6$	$9$	$-5$	$18$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+3q^{3}+4q^{4}+(-2-\beta _{2})q^{5}+\cdots$
174.4.a.i	$174$	$4$	174.a	1.a	$1$	$3$	$3$	$10.266$	3.3.717105.1	None	✓	$1$	$0$	$6$	$9$	$7$	$34$	$+$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+3q^{3}+4q^{4}+(2+\beta _{1})q^{5}+\cdots$
174.4.d.a	$174$	$4$	174.d	29.b	$2$	$6$	$6$	$10.266$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None		$2$	$0$	$0$	$0$	$22$	$-50$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+2\beta _{1}q^{2}+3\beta _{1}q^{3}-4q^{4}+(4-\beta _{3}+\cdots)q^{5}+\cdots$
174.4.d.b	$174$	$4$	174.d	29.b	$2$	$8$	$8$	$10.266$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$0$	$0$	$2$	$38$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-2\beta _{3}q^{2}+3\beta _{3}q^{3}-4q^{4}+(\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots$
174.4.f.a	$174$	$4$	174.f	87.f	$4$	$60$	$30$	$10.266$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
174.4.g.a	$174$	$4$	174.g	29.d	$7$	$6$	$1$	$10.266$	$\Q(\zeta_{14})$	None		$2$	$0$	$2$	$-3$	$28$	$52$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q-2\zeta_{14}^{4}q^{2}+(-3+3\zeta_{14}-3\zeta_{14}^{2}+\cdots)q^{3}+\cdots$
174.4.g.b	$174$	$4$	174.g	29.d	$7$	$18$	$3$	$10.266$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		$2$	$0$	$-6$	$9$	$29$	$-28$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q-2\beta _{8}q^{2}+3\beta _{11}q^{3}-4\beta _{10}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
174.4.g.c	$174$	$4$	174.g	29.d	$7$	$18$	$3$	$10.266$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		$2$	$0$	$6$	$-9$	$-37$	$-60$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(2-2\beta _{3}+2\beta _{4}-2\beta _{5}-2\beta _{6}-2\beta _{7}+\cdots)q^{2}+\cdots$
174.4.g.d	$174$	$4$	174.g	29.d	$7$	$24$	$4$	$10.266$		None		$2$	$0$	$-8$	$-12$	$-24$	$2$			$\mathrm{SU}(2)[C_{7}]$
174.4.g.e	$174$	$4$	174.g	29.d	$7$	$30$	$5$	$10.266$		None		$2$	$0$	$10$	$15$	$24$	$22$			$\mathrm{SU}(2)[C_{7}]$
174.4.h.a	$174$	$4$	174.h	29.e	$14$	$36$	$6$	$10.266$		None		$2$	$0$	$0$	$0$	$-22$	$64$			$\mathrm{SU}(2)[C_{14}]$
174.4.h.b	$174$	$4$	174.h	29.e	$14$	$48$	$8$	$10.266$		None		$2$	$0$	$0$	$0$	$-2$	$-52$			$\mathrm{SU}(2)[C_{14}]$
174.4.k.a	$174$	$4$	174.k	87.k	$28$	$360$	$30$	$10.266$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{28}]$
174.5.b.a	$174$	$5$	174.b	3.b	$2$	$36$	$36$	$17.986$		None		$2$	$0$	$0$	$12$	$0$	$-184$			$\mathrm{SU}(2)[C_{2}]$
174.5.c.a	$174$	$5$	174.c	87.d	$2$	$40$	$40$	$17.986$		None		$4$	$0$	$0$	$0$	$0$	$80$			$\mathrm{SU}(2)[C_{2}]$
174.5.e.a	$174$	$5$	174.e	29.c	$4$	$20$	$10$	$17.986$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$-40$	$0$	$0$	$96$		$2^{8}\cdot 3^{10}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2-2\beta _{5})q^{2}-\beta _{8}q^{3}+8\beta _{5}q^{4}+\cdots$

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 114 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.