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 90 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
574.2.a.a	$574$	$2$	574.a	1.a	$1$	$1$	$1$	$4.583$	$\Q$	None	✓	$1$	$0$	$-1$	$-2$	$4$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+4q^{5}+2q^{6}+q^{7}+\cdots$
574.2.a.b	$574$	$2$	574.a	1.a	$1$	$1$	$1$	$4.583$	$\Q$	None	✓	$1$	$1$	$-1$	$-1$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots$
574.2.a.c	$574$	$2$	574.a	1.a	$1$	$1$	$1$	$4.583$	$\Q$	None	✓	$1$	$1$	$-1$	$1$	$-3$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}+q^{7}+\cdots$
574.2.a.d	$574$	$2$	574.a	1.a	$1$	$1$	$1$	$4.583$	$\Q$	None	✓	$1$	$1$	$-1$	$2$	$-2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}-2q^{5}-2q^{6}-q^{7}+\cdots$
574.2.a.e	$574$	$2$	574.a	1.a	$1$	$1$	$1$	$4.583$	$\Q$	None	✓	$1$	$0$	$-1$	$2$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+2q^{3}+q^{4}+2q^{5}-2q^{6}+q^{7}+\cdots$
574.2.a.f	$574$	$2$	574.a	1.a	$1$	$1$	$1$	$4.583$	$\Q$	None	✓	$1$	$0$	$-1$	$3$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\cdots$
574.2.a.g	$574$	$2$	574.a	1.a	$1$	$1$	$1$	$4.583$	$\Q$	None	✓	$1$	$1$	$1$	$-3$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\cdots$
574.2.a.h	$574$	$2$	574.a	1.a	$1$	$1$	$1$	$4.583$	$\Q$	None	✓	$1$	$1$	$1$	$-1$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$
574.2.a.i	$574$	$2$	574.a	1.a	$1$	$1$	$1$	$4.583$	$\Q$	None	✓	$1$	$0$	$1$	$-1$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
574.2.a.j	$574$	$2$	574.a	1.a	$1$	$1$	$1$	$4.583$	$\Q$	None	✓	$1$	$1$	$1$	$0$	$-4$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-4q^{5}+q^{7}+q^{8}-3q^{9}+\cdots$
574.2.a.k	$574$	$2$	574.a	1.a	$1$	$2$	$2$	$4.583$	$\Q(\sqrt{3}) $	None	✓	$1$	$0$	$2$	$4$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}+(1+\beta )q^{5}+2q^{6}+\cdots$
574.2.a.l	$574$	$2$	574.a	1.a	$1$	$3$	$3$	$4.583$	3.3.568.1	None	✓	$1$	$0$	$3$	$1$	$1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots$
574.2.a.m	$574$	$2$	574.a	1.a	$1$	$4$	$4$	$4.583$	4.4.11348.1	None	✓	$1$	$0$	$-4$	$-1$	$3$	$-4$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-\beta _{2}q^{3}+q^{4}+(1-\beta _{2}+\beta _{3})q^{5}+\cdots$
574.2.c.a	$574$	$2$	574.c	41.b	$2$	$2$	$2$	$4.583$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+iq^{3}+q^{4}+q^{5}+iq^{6}+iq^{7}+\cdots$
574.2.c.b	$574$	$2$	574.c	41.b	$2$	$8$	$8$	$4.583$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$8$	$0$	$6$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{6})q^{5}+\beta _{1}q^{6}+\cdots$
574.2.c.c	$574$	$2$	574.c	41.b	$2$	$10$	$10$	$4.583$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None		$2$	$0$	$-10$	$0$	$-4$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{4}-\beta _{8})q^{5}+\cdots$
574.2.e.a	$574$	$2$	574.e	7.c	$3$	$2$	$1$	$4.583$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$-2$	$2$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
574.2.e.b	$574$	$2$	574.e	7.c	$3$	$2$	$1$	$4.583$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$1$	$1$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
574.2.e.c	$574$	$2$	574.e	7.c	$3$	$2$	$1$	$4.583$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$3$	$1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$
574.2.e.d	$574$	$2$	574.e	7.c	$3$	$4$	$2$	$4.583$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		$2$	$0$	$2$	$-1$	$1$	$-10$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{1})q^{2}-\beta _{3}q^{3}-\beta _{1}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots$
574.2.e.e	$574$	$2$	574.e	7.c	$3$	$6$	$3$	$4.583$	6.0.309123.1	None		$2$	$0$	$-3$	$3$	$-4$	$-4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{4})q^{2}+\beta _{4}q^{3}-\beta _{4}q^{4}+(-1+\cdots)q^{5}+\cdots$
574.2.e.f	$574$	$2$	574.e	7.c	$3$	$8$	$4$	$4.583$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None		$2$	$0$	$4$	$-4$	$-3$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+(-1+\beta _{2})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$
574.2.e.g	$574$	$2$	574.e	7.c	$3$	$12$	$6$	$4.583$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$6$	$-1$	$0$	$-1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{8}q^{2}+\beta _{2}q^{3}+(-1-\beta _{8})q^{4}+\beta _{10}q^{5}+\cdots$
574.2.e.h	$574$	$2$	574.e	7.c	$3$	$20$	$10$	$4.583$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$-10$	$1$	$-2$	$1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{10}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-1-\beta _{10}+\cdots)q^{4}+\cdots$
574.2.f.a	$574$	$2$	574.f	41.c	$4$	$20$	$10$	$4.583$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$0$	$-4$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{14}q^{2}+\beta _{13}q^{3}-q^{4}+\beta _{4}q^{5}+\cdots$
574.2.f.b	$574$	$2$	574.f	41.c	$4$	$24$	$12$	$4.583$		None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
574.2.h.a	$574$	$2$	574.h	41.d	$5$	$4$	$1$	$4.583$	$\Q(\zeta_{10})$	None		$2$	$0$	$-1$	$-2$	$1$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
574.2.h.b	$574$	$2$	574.h	41.d	$5$	$4$	$1$	$4.583$	$\Q(\zeta_{10})$	None		$2$	$0$	$-1$	$0$	$4$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots$
574.2.h.c	$574$	$2$	574.h	41.d	$5$	$4$	$1$	$4.583$	$\Q(\zeta_{10})$	None		$2$	$0$	$1$	$-12$	$-2$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-3q^{3}+\cdots$
574.2.h.d	$574$	$2$	574.h	41.d	$5$	$4$	$1$	$4.583$	$\Q(\zeta_{10})$	None		$2$	$0$	$1$	$2$	$6$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(1+\cdots)q^{3}+\cdots$
574.2.h.e	$574$	$2$	574.h	41.d	$5$	$4$	$1$	$4.583$	$\Q(\zeta_{10})$	None		$2$	$0$	$1$	$4$	$-2$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(2+\cdots)q^{3}+\cdots$
574.2.h.f	$574$	$2$	574.h	41.d	$5$	$4$	$1$	$4.583$	$\Q(\zeta_{10})$	None		$2$	$0$	$1$	$6$	$-1$	$1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(2+\cdots)q^{3}+\cdots$
574.2.h.g	$574$	$2$	574.h	41.d	$5$	$8$	$2$	$4.583$	8.0.4709390625.5	None		$2$	$0$	$-2$	$-4$	$3$	$-2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{4}q^{2}+(-\beta _{3}+\beta _{5})q^{3}+\beta _{5}q^{4}+\cdots$
574.2.h.h	$574$	$2$	574.h	41.d	$5$	$8$	$2$	$4.583$	8.0.123765625.1	None		$2$	$0$	$-2$	$-2$	$1$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{2}q^{2}+(-1-\beta _{3}+\beta _{4}-\beta _{7})q^{3}+\cdots$
574.2.h.i	$574$	$2$	574.h	41.d	$5$	$8$	$2$	$4.583$	8.0.511890625.1	None		$2$	$0$	$-2$	$12$	$-1$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{2}q^{2}+(1+\beta _{2}+\beta _{7})q^{3}+\beta _{4}q^{4}+\cdots$
574.2.h.j	$574$	$2$	574.h	41.d	$5$	$12$	$3$	$4.583$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$3$	$6$	$-4$	$-3$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+\beta _{6}q^{4}+\cdots$
574.2.h.k	$574$	$2$	574.h	41.d	$5$	$20$	$5$	$4.583$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		$2$	$0$	$5$	$-6$	$-1$	$5$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{4}q^{2}-\beta _{6}q^{3}+\beta _{3}q^{4}+\beta _{18}q^{5}+\cdots$
574.2.j.a	$574$	$2$	574.j	287.j	$6$	$28$	$14$	$4.583$		None		$4$	$0$	$-14$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
574.2.j.b	$574$	$2$	574.j	287.j	$6$	$28$	$14$	$4.583$		None		$4$	$0$	$14$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{6}]$
574.2.m.a	$574$	$2$	574.m	287.l	$8$	$56$	$14$	$4.583$		None		$4$	$0$	$0$	$0$	$0$	$-4$			$\mathrm{SU}(2)[C_{8}]$
574.2.m.b	$574$	$2$	574.m	287.l	$8$	$56$	$14$	$4.583$		None		$4$	$0$	$0$	$0$	$0$	$4$			$\mathrm{SU}(2)[C_{8}]$
574.2.n.a	$574$	$2$	574.n	41.f	$10$	$40$	$10$	$4.583$		None		$2$	$0$	$-10$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{10}]$
574.2.n.b	$574$	$2$	574.n	41.f	$10$	$40$	$10$	$4.583$		None		$2$	$0$	$10$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{10}]$
574.2.r.a	$574$	$2$	574.r	287.r	$12$	$8$	$2$	$4.583$	$\Q(\zeta_{24})$	None		$4$	$0$	$0$	$-4$	$0$	$12$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(\zeta_{24}^{2}-\zeta_{24}^{6})q^{2}+(-1+\zeta_{24}^{2}+\cdots)q^{3}+\cdots$
574.2.r.b	$574$	$2$	574.r	287.r	$12$	$8$	$2$	$4.583$	8.0.303595776.1	None		$4$	$0$	$0$	$-2$	$0$	$6$		$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	$q+\beta _{2}q^{2}+(\beta _{3}+\beta _{4}-\beta _{5})q^{3}-\beta _{4}q^{4}+\cdots$
574.2.r.c	$574$	$2$	574.r	287.r	$12$	$40$	$10$	$4.583$		None		$4$	$0$	$0$	$4$	$0$	$-12$			$\mathrm{SU}(2)[C_{12}]$
574.2.r.d	$574$	$2$	574.r	287.r	$12$	$56$	$14$	$4.583$		None		$4$	$0$	$0$	$2$	$0$	$-6$			$\mathrm{SU}(2)[C_{12}]$
574.2.s.a	$574$	$2$	574.s	287.s	$15$	$112$	$14$	$4.583$		None		$4$	$0$	$-14$	$2$	$0$	$2$			$\mathrm{SU}(2)[C_{15}]$
574.2.s.b	$574$	$2$	574.s	287.s	$15$	$112$	$14$	$4.583$		None		$4$	$0$	$14$	$-2$	$4$	$-2$			$\mathrm{SU}(2)[C_{15}]$
574.2.u.a	$574$	$2$	574.u	41.g	$20$	$80$	$10$	$4.583$		None		$2$	$0$	$0$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{20}]$

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 90 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.