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 99 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
418.2.a.a	$418$	$2$	418.a	1.a	$1$	$1$	$1$	$3.338$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$-2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-3q^{7}+\cdots$
418.2.a.b	$418$	$2$	418.a	1.a	$1$	$1$	$1$	$3.338$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}+2q^{7}+q^{8}-3q^{9}+\cdots$
418.2.a.c	$418$	$2$	418.a	1.a	$1$	$1$	$1$	$3.338$	$\Q$	None	✓	$1$	$0$	$1$	$3$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}+q^{4}-2q^{5}+3q^{6}+q^{7}+\cdots$
418.2.a.d	$418$	$2$	418.a	1.a	$1$	$2$	$2$	$3.338$	$\Q(\sqrt{13}) $	None	✓	$1$	$1$	$-2$	$-3$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(-1-\beta )q^{3}+q^{4}+(-1+\beta )q^{5}+\cdots$
418.2.a.e	$418$	$2$	418.a	1.a	$1$	$2$	$2$	$3.338$	$\Q(\sqrt{17}) $	None	✓	$1$	$0$	$-2$	$1$	$4$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+(1-\beta )q^{3}+q^{4}+2q^{5}+(-1+\cdots)q^{6}+\cdots$
418.2.a.f	$418$	$2$	418.a	1.a	$1$	$2$	$2$	$3.338$	$\Q(\sqrt{21}) $	None	✓	$1$	$0$	$2$	$-1$	$3$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta q^{3}+q^{4}+(2-\beta )q^{5}-\beta q^{6}+\cdots$
418.2.a.g	$418$	$2$	418.a	1.a	$1$	$3$	$3$	$3.338$	3.3.621.1	None	✓	$1$	$1$	$-3$	$0$	$-3$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1-\beta _{1}-\beta _{2})q^{5}+\cdots$
418.2.a.h	$418$	$2$	418.a	1.a	$1$	$3$	$3$	$3.338$	3.3.469.1	None	✓	$1$	$0$	$3$	$1$	$5$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(2-\beta _{1})q^{5}+\beta _{1}q^{6}+\cdots$
418.2.b.a	$418$	$2$	418.b	209.d	$2$	$2$	$2$	$3.338$	$\Q(\sqrt{-10}) $	None		$2$	$0$	$-2$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+q^{4}-2q^{5}+\beta q^{7}-q^{8}+3q^{9}+\cdots$
418.2.b.b	$418$	$2$	418.b	209.d	$2$	$2$	$2$	$3.338$	$\Q(\sqrt{-10}) $	None		$2$	$0$	$2$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+q^{4}-2q^{5}+\beta q^{7}+q^{8}+3q^{9}+\cdots$
418.2.b.c	$418$	$2$	418.b	209.d	$2$	$8$	$8$	$3.338$	8.0.$\cdots$.1	None		$2$	$0$	$-8$	$0$	$2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-\beta _{3}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{3}q^{6}+\cdots$
418.2.b.d	$418$	$2$	418.b	209.d	$2$	$8$	$8$	$3.338$	8.0.$\cdots$.1	None		$2$	$0$	$8$	$0$	$2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\beta _{3}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{3}q^{6}+\cdots$
418.2.e.a	$418$	$2$	418.e	19.c	$3$	$2$	$1$	$3.338$	$\Q(\sqrt{-3}) $	None		$2$	$1$	$-1$	$-2$	$-1$	$-6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
418.2.e.b	$418$	$2$	418.e	19.c	$3$	$2$	$1$	$3.338$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$-1$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots$
418.2.e.c	$418$	$2$	418.e	19.c	$3$	$2$	$1$	$3.338$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$4$	$-8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(4-4\zeta_{6})q^{5}+\cdots$
418.2.e.d	$418$	$2$	418.e	19.c	$3$	$2$	$1$	$3.338$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$2$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
418.2.e.e	$418$	$2$	418.e	19.c	$3$	$2$	$1$	$3.338$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$0$	$3$	$6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(3-3\zeta_{6})q^{5}+\cdots$
418.2.e.f	$418$	$2$	418.e	19.c	$3$	$2$	$1$	$3.338$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$2$	$3$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
418.2.e.g	$418$	$2$	418.e	19.c	$3$	$4$	$2$	$3.338$	$\Q(\sqrt{-2}, \sqrt{-3})$	None		$2$	$0$	$2$	$0$	$0$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-1+\beta _{1})q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots$
418.2.e.h	$418$	$2$	418.e	19.c	$3$	$6$	$3$	$3.338$	6.0.591408.1	None		$2$	$0$	$-3$	$2$	$-2$	$8$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{4}q^{2}+(-\beta _{1}+\beta _{4})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots$
418.2.e.i	$418$	$2$	418.e	19.c	$3$	$6$	$3$	$3.338$	6.0.101617200.1	None		$2$	$0$	$3$	$0$	$-6$	$12$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{4}q^{2}-\beta _{1}q^{3}+(-1+\beta _{4})q^{4}-2\beta _{4}q^{5}+\cdots$
418.2.f.a	$418$	$2$	418.f	11.c	$5$	$4$	$1$	$3.338$	$\Q(\zeta_{10})$	None		$2$	$1$	$-1$	$-4$	$-8$	$-7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
418.2.f.b	$418$	$2$	418.f	11.c	$5$	$4$	$1$	$3.338$	$\Q(\zeta_{10})$	None		$2$	$0$	$-1$	$0$	$8$	$3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
418.2.f.c	$418$	$2$	418.f	11.c	$5$	$4$	$1$	$3.338$	$\Q(\zeta_{10})$	None		$2$	$0$	$-1$	$1$	$-1$	$-3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
418.2.f.d	$418$	$2$	418.f	11.c	$5$	$4$	$1$	$3.338$	$\Q(\zeta_{10})$	None		$2$	$0$	$-1$	$2$	$2$	$9$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
418.2.f.e	$418$	$2$	418.f	11.c	$5$	$4$	$1$	$3.338$	$\Q(\zeta_{10})$	None		$2$	$0$	$-1$	$5$	$3$	$-7$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
418.2.f.f	$418$	$2$	418.f	11.c	$5$	$16$	$4$	$3.338$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-4$	$0$	$4$	$6$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{4}q^{2}+(-1+\beta _{1}+\beta _{2}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots$
418.2.f.g	$418$	$2$	418.f	11.c	$5$	$16$	$4$	$3.338$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$4$	$1$	$1$	$-12$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1+\beta _{6}-\beta _{8}+\beta _{10})q^{2}+\beta _{1}q^{3}+\cdots$
418.2.f.h	$418$	$2$	418.f	11.c	$5$	$20$	$5$	$3.338$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$5$	$-1$	$-1$	$13$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{9}q^{2}-\beta _{4}q^{3}+(-1+\beta _{8}+\beta _{9}+\cdots)q^{4}+\cdots$
418.2.h.a	$418$	$2$	418.h	209.g	$6$	$20$	$10$	$3.338$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$-10$	$3$	$2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{10}q^{2}+\beta _{3}q^{3}+(-1+\beta _{10})q^{4}+\cdots$
418.2.h.b	$418$	$2$	418.h	209.g	$6$	$20$	$10$	$3.338$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$10$	$3$	$2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\beta _{10})q^{2}+\beta _{4}q^{3}-\beta _{10}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
418.2.j.a	$418$	$2$	418.j	19.e	$9$	$24$	$4$	$3.338$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{9}]$
418.2.j.b	$418$	$2$	418.j	19.e	$9$	$24$	$4$	$3.338$		None		$2$	$0$	$0$	$0$	$0$	$12$			$\mathrm{SU}(2)[C_{9}]$
418.2.j.c	$418$	$2$	418.j	19.e	$9$	$30$	$5$	$3.338$		None		$2$	$0$	$0$	$0$	$0$	$-12$			$\mathrm{SU}(2)[C_{9}]$
418.2.j.d	$418$	$2$	418.j	19.e	$9$	$30$	$5$	$3.338$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{9}]$
418.2.m.a	$418$	$2$	418.m	209.k	$10$	$40$	$10$	$3.338$		None		$2$	$0$	$-10$	$0$	$2$	$-5$			$\mathrm{SU}(2)[C_{10}]$
418.2.m.b	$418$	$2$	418.m	209.k	$10$	$40$	$10$	$3.338$		None		$2$	$0$	$10$	$0$	$2$	$-5$			$\mathrm{SU}(2)[C_{10}]$
418.2.n.a	$418$	$2$	418.n	209.n	$15$	$8$	$1$	$3.338$	$\Q(\zeta_{15})$	None		$4$	$0$	$-1$	$6$	$7$	$-2$		$1$	$\mathrm{SU}(2)[C_{15}]$	$q+(\zeta_{15}+\zeta_{15}^{6})q^{2}+(2\zeta_{15}-2\zeta_{15}^{5}+\cdots)q^{3}+\cdots$
418.2.n.b	$418$	$2$	418.n	209.n	$15$	$8$	$1$	$3.338$	$\Q(\zeta_{15})$	None		$4$	$0$	$1$	$-2$	$-5$	$6$		$1$	$\mathrm{SU}(2)[C_{15}]$	$q+(-\zeta_{15}-\zeta_{15}^{6})q^{2}+(2-2\zeta_{15}+2\zeta_{15}^{3}+\cdots)q^{3}+\cdots$
418.2.n.c	$418$	$2$	418.n	209.n	$15$	$8$	$1$	$3.338$	$\Q(\zeta_{15})$	None		$4$	$0$	$1$	$2$	$1$	$6$		$1$	$\mathrm{SU}(2)[C_{15}]$	$q+(-\zeta_{15}-\zeta_{15}^{6})q^{2}+(-2+2\zeta_{15}+\cdots)q^{3}+\cdots$
418.2.n.d	$418$	$2$	418.n	209.n	$15$	$64$	$8$	$3.338$		None		$4$	$0$	$-8$	$-6$	$-7$	$22$			$\mathrm{SU}(2)[C_{15}]$
418.2.n.e	$418$	$2$	418.n	209.n	$15$	$72$	$9$	$3.338$		None		$4$	$0$	$9$	$-2$	$8$	$-20$			$\mathrm{SU}(2)[C_{15}]$
418.2.q.a	$418$	$2$	418.q	209.p	$18$	$60$	$10$	$3.338$		None		$2$	$0$	$0$	$-3$	$0$	$-18$			$\mathrm{SU}(2)[C_{18}]$
418.2.q.b	$418$	$2$	418.q	209.p	$18$	$60$	$10$	$3.338$		None		$2$	$0$	$0$	$-3$	$0$	$18$			$\mathrm{SU}(2)[C_{18}]$
418.2.s.a	$418$	$2$	418.s	209.t	$30$	$80$	$10$	$3.338$		None		$2$	$0$	$-10$	$-3$	$-2$	$-10$			$\mathrm{SU}(2)[C_{30}]$
418.2.s.b	$418$	$2$	418.s	209.t	$30$	$80$	$10$	$3.338$		None		$2$	$0$	$10$	$-3$	$-2$	$-10$			$\mathrm{SU}(2)[C_{30}]$
418.2.u.a	$418$	$2$	418.u	209.u	$45$	$216$	$9$	$3.338$		None		$4$	$0$	$0$	$0$	$0$	$-3$			$\mathrm{SU}(2)[C_{45}]$
418.2.u.b	$418$	$2$	418.u	209.u	$45$	$264$	$11$	$3.338$		None		$4$	$0$	$0$	$6$	$0$	$-15$			$\mathrm{SU}(2)[C_{45}]$
418.2.v.a	$418$	$2$	418.v	209.w	$90$	$240$	$10$	$3.338$		None		$2$	$0$	$0$	$3$	$0$	$33$			$\mathrm{SU}(2)[C_{90}]$
418.2.v.b	$418$	$2$	418.v	209.w	$90$	$240$	$10$	$3.338$		None		$2$	$0$	$0$	$3$	$0$	$-3$			$\mathrm{SU}(2)[C_{90}]$

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 99 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.