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 74 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
125.2.a.a	$125$	$2$	125.a	1.a	$1$	$2$	$2$	$0.998$	$\Q(\sqrt{5}) $	None	✓	$1$	$1$	$-1$	$-3$	$0$	$-6$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(-2+\beta )q^{3}+(-1+\beta )q^{4}+\cdots$
125.2.a.b	$125$	$2$	125.a	1.a	$1$	$2$	$2$	$0.998$	$\Q(\sqrt{5}) $	None	✓	$1$	$0$	$1$	$3$	$0$	$6$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(2-\beta )q^{3}+(-1+\beta )q^{4}+(-1+\cdots)q^{6}+\cdots$
125.2.a.c	$125$	$2$	125.a	1.a	$1$	$4$	$4$	$0.998$	4.4.4400.1	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{3}q^{2}-\beta _{1}q^{3}+(1-2\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots$
125.2.b.a	$125$	$2$	125.b	5.b	$2$	$4$	$4$	$0.998$	4.0.4400.1	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-\beta _{1}q^{3}+(-1-2\beta _{2})q^{4}+\cdots$
125.2.b.b	$125$	$2$	125.b	5.b	$2$	$4$	$4$	$0.998$	$\Q(i, \sqrt{5})$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{1}+2\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$
125.2.d.a	$125$	$2$	125.d	25.d	$5$	$4$	$1$	$0.998$	$\Q(\zeta_{10})$	None		$2$	$0$	$2$	$1$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots$
125.2.d.b	$125$	$2$	125.d	25.d	$5$	$16$	$4$	$0.998$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$		$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{6}q^{2}+(\beta _{6}+\beta _{12}+\beta _{13}-\beta _{14}+\cdots)q^{3}+\cdots$
125.2.e.a	$125$	$2$	125.e	25.e	$10$	$8$	$2$	$0.998$	$\Q(\zeta_{20})$	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(-\zeta_{20}+\zeta_{20}^{3}-\zeta_{20}^{5})q^{2}-\zeta_{20}q^{3}+\cdots$
125.2.e.b	$125$	$2$	125.e	25.e	$10$	$8$	$2$	$0.998$	8.0.58140625.2	None		$2$	$0$	$5$	$5$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{10}]$	$q+(1-\beta _{1})q^{2}+(1-\beta _{2}+\beta _{3}-\beta _{7})q^{3}+\cdots$
125.2.g.a	$125$	$2$	125.g	125.g	$25$	$220$	$11$	$0.998$		None		$2$	$0$	$-20$	$-20$	$-15$	$-15$			$\mathrm{SU}(2)[C_{25}]$
125.2.h.a	$125$	$2$	125.h	125.h	$50$	$240$	$12$	$0.998$		None		$2$	$0$	$-20$	$-20$	$-25$	$-25$			$\mathrm{SU}(2)[C_{50}]$
125.3.c.a	$125$	$3$	125.c	5.c	$4$	$16$	$8$	$3.406$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}\cdot 5^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+(\beta _{11}+\beta _{12})q^{3}+(-\beta _{7}-\beta _{10}+\cdots)q^{4}+\cdots$
125.3.c.b	$125$	$3$	125.c	5.c	$4$	$16$	$8$	$3.406$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		$4$	$0$	$0$	$0$	$0$	$0$		$5^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{4}q^{2}+\beta _{13}q^{3}+(3\beta _{7}+\beta _{12})q^{4}+\cdots$
125.3.f.a	$125$	$3$	125.f	25.f	$20$	$32$	$4$	$3.406$		None		$2$	$0$	$0$	$0$	$0$	$-10$			$\mathrm{SU}(2)[C_{20}]$
125.3.f.b	$125$	$3$	125.f	25.f	$20$	$32$	$4$	$3.406$		None		$2$	$0$	$0$	$0$	$0$	$10$			$\mathrm{SU}(2)[C_{20}]$
125.3.f.c	$125$	$3$	125.f	25.f	$20$	$32$	$4$	$3.406$		None		$2$	$0$	$10$	$10$	$0$	$10$			$\mathrm{SU}(2)[C_{20}]$
125.3.i.a	$125$	$3$	125.i	125.i	$100$	$960$	$24$	$3.406$		None		$2$	$0$	$-40$	$-40$	$-40$	$-40$			$\mathrm{SU}(2)[C_{100}]$
125.4.a.a	$125$	$4$	125.a	1.a	$1$	$4$	$4$	$7.375$	4.4.12400.1	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-1+2\beta _{2}+\cdots)q^{4}+\cdots$
125.4.a.b	$125$	$4$	125.a	1.a	$1$	$6$	$6$	$7.375$	6.6.497918125.1	None	✓	$1$	$1$	$-7$	$-14$	$0$	$-67$	$-$	$5^{2}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{2})q^{2}+(-2-\beta _{1})q^{3}+(5+\cdots)q^{4}+\cdots$
125.4.a.c	$125$	$4$	125.a	1.a	$1$	$6$	$6$	$7.375$	6.6.497918125.1	None	✓	$1$	$0$	$7$	$14$	$0$	$67$	$+$	$5^{2}$	$\mathrm{SU}(2)$	$q+(1-\beta _{2})q^{2}+(2+\beta _{1})q^{3}+(5-\beta _{2}+\cdots)q^{4}+\cdots$
125.4.a.d	$125$	$4$	125.a	1.a	$1$	$8$	$8$	$7.375$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$2^{2}\cdot 5^{4}$	$\mathrm{SU}(2)$	$q-\beta _{5}q^{2}+\beta _{4}q^{3}+(5-\beta _{3})q^{4}+(5-\beta _{1}+\cdots)q^{6}+\cdots$
125.4.b.a	$125$	$4$	125.b	5.b	$2$	$4$	$4$	$7.375$	4.0.12400.1	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+(1+2\beta _{2})q^{4}+\cdots$
125.4.b.b	$125$	$4$	125.b	5.b	$2$	$8$	$8$	$7.375$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$5^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{2}+\beta _{4}q^{3}+(-5-\beta _{3})q^{4}+(5+\cdots)q^{6}+\cdots$
125.4.b.c	$125$	$4$	125.b	5.b	$2$	$12$	$12$	$7.375$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$5^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}+\beta _{5}q^{3}+(-6-\beta _{2})q^{4}+(-3+\cdots)q^{6}+\cdots$
125.4.d.a	$125$	$4$	125.d	25.d	$5$	$28$	$7$	$7.375$		None		$2$	$0$	$1$	$7$	$0$	$16$			$\mathrm{SU}(2)[C_{5}]$
125.4.d.b	$125$	$4$	125.d	25.d	$5$	$48$	$12$	$7.375$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{5}]$
125.4.e.a	$125$	$4$	125.e	25.e	$10$	$24$	$6$	$7.375$		None		$2$	$0$	$5$	$5$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
125.4.e.b	$125$	$4$	125.e	25.e	$10$	$56$	$14$	$7.375$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
125.4.g.a	$125$	$4$	125.g	125.g	$25$	$740$	$37$	$7.375$		None		$2$	$0$	$-20$	$-20$	$0$	$-15$			$\mathrm{SU}(2)[C_{25}]$
125.4.h.a	$125$	$4$	125.h	125.h	$50$	$720$	$36$	$7.375$		None		$2$	$0$	$-20$	$-20$	$-40$	$-25$			$\mathrm{SU}(2)[C_{50}]$
125.5.c.a	$125$	$5$	125.c	5.c	$4$	$32$	$16$	$12.921$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
125.5.c.b	$125$	$5$	125.c	5.c	$4$	$32$	$16$	$12.921$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
125.5.f.a	$125$	$5$	125.f	25.f	$20$	$72$	$9$	$12.921$		None		$2$	$0$	$-2$	$-12$	$0$	$-42$			$\mathrm{SU}(2)[C_{20}]$
125.5.f.b	$125$	$5$	125.f	25.f	$20$	$72$	$9$	$12.921$		None		$2$	$0$	$2$	$12$	$0$	$42$			$\mathrm{SU}(2)[C_{20}]$
125.5.f.c	$125$	$5$	125.f	25.f	$20$	$72$	$9$	$12.921$		None		$2$	$0$	$8$	$-2$	$0$	$-42$			$\mathrm{SU}(2)[C_{20}]$
125.5.i.a	$125$	$5$	125.i	125.i	$100$	$1960$	$49$	$12.921$		None		$2$	$0$	$-40$	$-40$	$-40$	$-40$			$\mathrm{SU}(2)[C_{100}]$
125.6.a.a	$125$	$6$	125.a	1.a	$1$	$8$	$8$	$20.048$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$+$	$2^{4}\cdot 5^{4}$	$\mathrm{SU}(2)$	$q+\beta _{6}q^{2}+(-\beta _{1}-\beta _{6})q^{3}+(4-2\beta _{2}+\cdots)q^{4}+\cdots$
125.6.a.b	$125$	$6$	125.a	1.a	$1$	$10$	$10$	$20.048$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$1$	$-9$	$-47$	$0$	$-394$	$+$	$2^{2}\cdot 5^{8}$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(-5-\beta _{7})q^{3}+(15+\cdots)q^{4}+\cdots$
125.6.a.c	$125$	$6$	125.a	1.a	$1$	$10$	$10$	$20.048$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	$1$	$0$	$9$	$47$	$0$	$394$	$-$	$2^{2}\cdot 5^{8}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(5+\beta _{7})q^{3}+(15-2\beta _{1}+\cdots)q^{4}+\cdots$
125.6.a.d	$125$	$6$	125.a	1.a	$1$	$12$	$12$	$20.048$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$-$	$2^{8}\cdot 5^{12}$	$\mathrm{SU}(2)$	$q-\beta _{7}q^{2}-\beta _{6}q^{3}+(26+\beta _{1}-\beta _{2})q^{4}+\cdots$
125.6.b.a	$125$	$6$	125.b	5.b	$2$	$8$	$8$	$20.048$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$5^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{7})q^{3}+(-4-2\beta _{2}+\cdots)q^{4}+\cdots$
125.6.b.b	$125$	$6$	125.b	5.b	$2$	$12$	$12$	$20.048$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{8}\cdot 5^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{2}-\beta _{6}q^{3}+(-26+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
125.6.b.c	$125$	$6$	125.b	5.b	$2$	$20$	$20$	$20.048$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 5^{38}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{10}q^{2}+\beta _{13}q^{3}+(-14-\beta _{1})q^{4}+\cdots$
125.7.c.a	$125$	$7$	125.c	5.c	$4$	$48$	$24$	$28.757$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
125.7.c.b	$125$	$7$	125.c	5.c	$4$	$48$	$24$	$28.757$		None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
125.8.a.a	$125$	$8$	125.a	1.a	$1$	$12$	$12$	$39.048$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	$2$	$1$	$0$	$0$	$0$	$0$	$-$	$2^{8}\cdot 5^{12}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{8})q^{3}+(6^{2}+4\beta _{2}+\cdots)q^{4}+\cdots$
125.8.a.b	$125$	$8$	125.a	1.a	$1$	$14$	$14$	$39.048$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$1$	$-3$	$-101$	$0$	$-2658$	$-$	$2^{8}\cdot 3^{2}\cdot 5^{17}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(-7+\beta _{6})q^{3}+(60+2\beta _{1}+\cdots)q^{4}+\cdots$
125.8.a.c	$125$	$8$	125.a	1.a	$1$	$14$	$14$	$39.048$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	None	✓	$1$	$0$	$3$	$101$	$0$	$2658$	$+$	$2^{8}\cdot 3^{2}\cdot 5^{17}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(7-\beta _{6})q^{3}+(60+2\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$
125.8.a.d	$125$	$8$	125.a	1.a	$1$	$16$	$16$	$39.048$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$+$	$2^{16}\cdot 5^{22}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{10}q^{3}+(87+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
125.8.b.a	$125$	$8$	125.b	5.b	$2$	$12$	$12$	$39.048$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}\cdot 5^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{8})q^{3}+(-6^{2}-4\beta _{2}+\cdots)q^{4}+\cdots$

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 74 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.