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 106 matches)

Next Download displayed columns for results to

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	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	CM	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
69.2.a.a	$69$	$2$	69.a	1.a	$1$	$1$	$1$	$0.551$	$\Q$	None	✓	✓	✓	✓	69.2.a.a	$1$	$0$	$1$	$1$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+q^{6}-2q^{7}-3q^{8}+\cdots$
69.2.a.b	$69$	$2$	69.a	1.a	$1$	$2$	$2$	$0.551$	$\Q(\sqrt{5}) $	None	✓	✓	✓	✓	69.2.a.b	$1$	$0$	$0$	$-2$	$-2$	$2$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{2}-q^{3}+3q^{4}+(-1+\beta )q^{5}+\cdots$
69.2.c.a	$69$	$2$	69.c	69.c	$2$	$6$	$6$	$0.551$	6.0.8869743.1	$\Q(\sqrt{-23}) $		✓	✓	✓	69.2.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-2+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$
69.2.e.a	$69$	$2$	69.e	23.c	$11$	$10$	$1$	$0.551$	$\Q(\zeta_{22})$	None		✓			69.2.e.a	$2$	$0$	$-4$	$1$	$5$	$-8$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(-1+\zeta_{22}-\zeta_{22}^{2}-\zeta_{22}^{4}-\zeta_{22}^{6}+\cdots)q^{2}+\cdots$
69.2.e.b	$69$	$2$	69.e	23.c	$11$	$10$	$1$	$0.551$	$\Q(\zeta_{22})$	None		✓			69.2.e.b	$2$	$0$	$4$	$1$	$-3$	$6$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(-\zeta_{22}^{4}+\zeta_{22}^{5}-\zeta_{22}^{8}+\zeta_{22}^{9})q^{2}+\cdots$
69.2.e.c	$69$	$2$	69.e	23.c	$11$	$20$	$2$	$0.551$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓	✓		69.2.e.c	$2$	$0$	$-4$	$-2$	$-6$	$-6$		$1$	$\mathrm{SU}(2)[C_{11}]$	$q+(\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+2\beta _{6}+2\beta _{7}+\cdots)q^{2}+\cdots$
69.2.g.a	$69$	$2$	69.g	69.g	$22$	$60$	$6$	$0.551$		None		✓	✓	✓	69.2.g.a	$4$	$0$	$0$	$-11$	$0$	$-22$			$\mathrm{SU}(2)[C_{22}]$
69.3.b.a	$69$	$3$	69.b	3.b	$2$	$14$	$14$	$1.880$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None		✓	✓	✓	69.3.b.a	$2$	$0$	$0$	$-4$	$0$	$-4$		$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{8}q^{3}+(-2+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots$
69.3.d.a	$69$	$3$	69.d	23.b	$2$	$8$	$8$	$1.880$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None		✓	✓	✓	69.3.d.a	$2$	$0$	$-4$	$0$	$0$	$0$		$2^{3}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{2}+\beta _{3})q^{2}+\beta _{3}q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$
69.3.f.a	$69$	$3$	69.f	23.d	$22$	$80$	$8$	$1.880$		None		✓	✓	✓	69.3.f.a	$2$	$0$	$4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
69.3.h.a	$69$	$3$	69.h	69.h	$22$	$140$	$14$	$1.880$		None		✓	✓	✓	69.3.h.a	$4$	$0$	$0$	$-7$	$0$	$-18$			$\mathrm{SU}(2)[C_{22}]$
69.4.a.a	$69$	$4$	69.a	1.a	$1$	$2$	$2$	$4.071$	$\Q(\sqrt{5}) $	None	✓	✓	✓	✓	69.4.a.a	$1$	$1$	$-4$	$6$	$-26$	$-10$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-2-\beta )q^{2}+3q^{3}+(1+4\beta )q^{4}+\cdots$
69.4.a.b	$69$	$4$	69.a	1.a	$1$	$2$	$2$	$4.071$	$\Q(\sqrt{2}) $	None	✓	✓	✓	✓	69.4.a.b	$1$	$1$	$-2$	$-6$	$8$	$-28$	$-$	$2$	$\mathrm{SU}(2)$	$q+(-1+\beta )q^{2}-3q^{3}+(1-2\beta )q^{4}+\cdots$
69.4.a.c	$69$	$4$	69.a	1.a	$1$	$4$	$4$	$4.071$	4.4.1140200.1	None	✓	✓	✓	✓	69.4.a.c	$1$	$0$	$-2$	$-12$	$-2$	$32$	$+$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-3q^{3}+(6-\beta _{1}-2\beta _{2})q^{4}+\cdots$
69.4.a.d	$69$	$4$	69.a	1.a	$1$	$4$	$4$	$4.071$	4.4.2009704.1	None	✓	✓	✓	✓	69.4.a.d	$1$	$0$	$4$	$12$	$4$	$-14$	$+$	$2$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+3q^{3}+(7-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
69.4.c.a	$69$	$4$	69.c	69.c	$2$	$2$	$2$	$4.071$	$\Q(\sqrt{-23}) $	$\Q(\sqrt{-23}) $		✓			69.4.c.a	$4$	$0$	$0$	$4$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{2}+(2-\beta )q^{3}-15q^{4}+(-23+\cdots)q^{6}+\cdots$
69.4.c.b	$69$	$4$	69.c	69.c	$2$	$4$	$4$	$4.071$	$\Q(\sqrt{-3}, \sqrt{-23})$	$\Q(\sqrt{-23}) $		✓			69.4.c.b	$4$	$0$	$0$	$-4$	$0$	$0$		$3$	$\mathrm{U}(1)[D_{2}]$	$q+(-1-\beta _{2}-\beta _{3})q^{2}+(-1+2\beta _{1}+\cdots)q^{3}+\cdots$
69.4.c.c	$69$	$4$	69.c	69.c	$2$	$16$	$16$	$4.071$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		✓	✓		69.4.c.c	$4$	$0$	$0$	$-6$	$0$	$0$		$2^{9}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{11}q^{2}-\beta _{10}q^{3}+(-2+\beta _{1})q^{4}+\cdots$
69.4.e.a	$69$	$4$	69.e	23.c	$11$	$60$	$6$	$4.071$		None		✓			69.4.e.a	$2$	$0$	$0$	$-18$	$22$	$24$			$\mathrm{SU}(2)[C_{11}]$
69.4.e.b	$69$	$4$	69.e	23.c	$11$	$60$	$6$	$4.071$		None		✓			69.4.e.b	$2$	$0$	$4$	$18$	$-6$	$-4$			$\mathrm{SU}(2)[C_{11}]$
69.4.g.a	$69$	$4$	69.g	69.g	$22$	$220$	$22$	$4.071$		None		✓	✓	✓	69.4.g.a	$4$	$0$	$0$	$-5$	$0$	$-22$			$\mathrm{SU}(2)[C_{22}]$
69.5.b.a	$69$	$5$	69.b	3.b	$2$	$30$	$30$	$7.133$		None		✓	✓	✓	69.5.b.a	$2$	$0$	$0$	$8$	$0$	$-4$			$\mathrm{SU}(2)[C_{2}]$
69.5.d.a	$69$	$5$	69.d	23.b	$2$	$16$	$16$	$7.133$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓	✓	✓	69.5.d.a	$2$	$0$	$12$	$0$	$0$	$0$		$2^{6}\cdot 3^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{2})q^{2}+\beta _{3}q^{3}+(9+\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots$
69.5.f.a	$69$	$5$	69.f	23.d	$22$	$160$	$16$	$7.133$		None		✓	✓	✓	69.5.f.a	$2$	$0$	$-12$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
69.5.h.a	$69$	$5$	69.h	69.h	$22$	$300$	$30$	$7.133$		None		✓	✓	✓	69.5.h.a	$4$	$0$	$0$	$-19$	$0$	$-18$			$\mathrm{SU}(2)[C_{22}]$
69.6.a.a	$69$	$6$	69.a	1.a	$1$	$2$	$2$	$11.066$	$\Q(\sqrt{29}) $	None	✓	✓			69.6.a.a	$1$	$0$	$0$	$-18$	$94$	$-118$	$-$	$2$	$\mathrm{SU}(2)$	$q-2\beta q^{2}-9q^{3}+84q^{4}+(47-\beta )q^{5}+\cdots$
69.6.a.b	$69$	$6$	69.a	1.a	$1$	$3$	$3$	$11.066$	3.3.5333.1	None	✓	✓	✓	✓	69.6.a.b	$1$	$1$	$-8$	$27$	$-56$	$-114$	$+$	$2$	$\mathrm{SU}(2)$	$q+(-3+\beta _{2})q^{2}+9q^{3}+(9-4\beta _{1}-9\beta _{2})q^{4}+\cdots$
69.6.a.c	$69$	$6$	69.a	1.a	$1$	$4$	$4$	$11.066$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	✓	✓		69.6.a.c	$1$	$0$	$4$	$-36$	$-122$	$62$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1+\beta _{1})q^{2}-9q^{3}+(-12+4\beta _{1}+\cdots)q^{4}+\cdots$
69.6.a.d	$69$	$6$	69.a	1.a	$1$	$4$	$4$	$11.066$	$\mathbb{Q}[x]/(x^{4} - \cdots)$	None	✓	✓	✓	✓	69.6.a.d	$1$	$1$	$4$	$-36$	$22$	$-62$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}-9q^{3}+(7-\beta _{1}+\beta _{3})q^{4}+\cdots$
69.6.a.e	$69$	$6$	69.a	1.a	$1$	$5$	$5$	$11.066$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	✓	✓	✓	69.6.a.e	$1$	$0$	$8$	$45$	$94$	$272$	$-$	$2^{5}$	$\mathrm{SU}(2)$	$q+(2-\beta _{2})q^{2}+9q^{3}+(24-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
69.6.c.a	$69$	$6$	69.c	69.c	$2$	$6$	$6$	$11.066$	6.0.8869743.1	$\Q(\sqrt{-23}) $		✓			69.6.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q+(-\beta _{1}-3\beta _{2}-2\beta _{3}+\beta _{4}+\beta _{5})q^{2}+\cdots$
69.6.c.b	$69$	$6$	69.c	69.c	$2$	$32$	$32$	$11.066$		None		✓	✓		69.6.c.b	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
69.6.e.a	$69$	$6$	69.e	23.c	$11$	$100$	$10$	$11.066$		None		✓			69.6.e.a	$2$	$0$	$-8$	$90$	$6$	$118$			$\mathrm{SU}(2)[C_{11}]$
69.6.e.b	$69$	$6$	69.e	23.c	$11$	$100$	$10$	$11.066$		None		✓			69.6.e.b	$2$	$0$	$12$	$-90$	$-50$	$-78$			$\mathrm{SU}(2)[C_{11}]$
69.6.g.a	$69$	$6$	69.g	69.g	$22$	$380$	$38$	$11.066$		None		✓	✓	✓	69.6.g.a	$4$	$0$	$0$	$-11$	$0$	$-22$			$\mathrm{SU}(2)[C_{22}]$
69.7.b.a	$69$	$7$	69.b	3.b	$2$	$44$	$44$	$15.874$		None		✓	✓	✓	69.7.b.a	$2$	$0$	$0$	$20$	$0$	$568$			$\mathrm{SU}(2)[C_{2}]$
69.7.d.a	$69$	$7$	69.d	23.b	$2$	$24$	$24$	$15.874$		None		✓	✓	✓	69.7.d.a	$2$	$0$	$-20$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
69.7.f.a	$69$	$7$	69.f	23.d	$22$	$240$	$24$	$15.874$		None		✓	✓	✓	69.7.f.a	$2$	$0$	$20$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{22}]$
69.7.h.a	$69$	$7$	69.h	69.h	$22$	$460$	$46$	$15.874$		None		✓	✓	✓	69.7.h.a	$4$	$0$	$0$	$23$	$0$	$-18$			$\mathrm{SU}(2)[C_{22}]$
69.8.a.a	$69$	$8$	69.a	1.a	$1$	$5$	$5$	$21.555$	$\mathbb{Q}[x]/(x^{5} - \cdots)$	None	✓	✓	✓	✓	69.8.a.a	$1$	$1$	$0$	$-135$	$-266$	$-496$	$-$	$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-3^{3}q^{3}+(54+2\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots$
69.8.a.b	$69$	$8$	69.a	1.a	$1$	$6$	$6$	$21.555$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None	✓	✓	✓	✓	69.8.a.b	$1$	$1$	$-8$	$162$	$-372$	$-1104$	$-$	$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{2}+3^{3}q^{3}+(29+3\beta _{1}+\cdots)q^{4}+\cdots$
69.8.a.c	$69$	$8$	69.a	1.a	$1$	$7$	$7$	$21.555$	$\mathbb{Q}[x]/(x^{7} - \cdots)$	None	✓	✓	✓	✓	69.8.a.c	$1$	$0$	$0$	$-189$	$-516$	$1018$	$+$	$2^{5}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-3^{3}q^{3}+(93+\beta _{1}+\beta _{2})q^{4}+\cdots$
69.8.a.d	$69$	$8$	69.a	1.a	$1$	$8$	$8$	$21.555$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None	✓	✓	✓	✓	69.8.a.d	$1$	$0$	$24$	$216$	$378$	$126$	$+$	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)$	$q+(3-\beta _{1})q^{2}+3^{3}q^{3}+(70-4\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
69.8.c.a	$69$	$8$	69.c	69.c	$2$	$6$	$6$	$21.555$	6.0.8869743.1	$\Q(\sqrt{-23}) $		✓			69.8.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q+(-2\beta _{1}-6\beta _{2}+3\beta _{3}+2\beta _{4}+2\beta _{5})q^{2}+\cdots$
69.8.c.b	$69$	$8$	69.c	69.c	$2$	$48$	$48$	$21.555$		None		✓	✓		69.8.c.b	$4$	$0$	$0$	$24$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
69.8.e.a	$69$	$8$	69.e	23.c	$11$	$140$	$14$	$21.555$		None		✓			69.8.e.a	$2$	$0$	$-16$	$-378$	$-6$	$978$			$\mathrm{SU}(2)[C_{11}]$
69.8.e.b	$69$	$8$	69.e	23.c	$11$	$140$	$14$	$21.555$		None		✓			69.8.e.b	$2$	$0$	$-12$	$378$	$2$	$-394$			$\mathrm{SU}(2)[C_{11}]$
69.8.g.a	$69$	$8$	69.g	69.g	$22$	$540$	$54$	$21.555$		None		✓	✓	✓	69.8.g.a	$4$	$0$	$0$	$-35$	$0$	$-22$			$\mathrm{SU}(2)[C_{22}]$
69.9.b.a	$69$	$9$	69.b	3.b	$2$	$58$	$58$	$28.109$		None		✓	✓	✓	69.9.b.a	$2$	$0$	$0$	$-112$	$0$	$6996$			$\mathrm{SU}(2)[C_{2}]$
69.9.d.a	$69$	$9$	69.d	23.b	$2$	$32$	$32$	$28.109$		None		✓	✓	✓	69.9.d.a	$2$	$0$	$12$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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 106 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.