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 163 matches)

Next Download displayed columns for results to

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	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	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
52.1.j.a	$52$	$1$	52.j	52.j	$6$	$2$	$1$	$0.026$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
52.2.a.a	$52$	$2$	52.a	1.a	$1$	$1$	$1$	$0.415$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{5}-2q^{7}-3q^{9}-2q^{11}-q^{13}+\cdots$
52.2.e.a	$52$	$2$	52.e	13.c	$3$	$2$	$1$	$0.415$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-3$	$4$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-3+3\zeta_{6})q^{3}+2q^{5}-\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots$
52.2.e.b	$52$	$2$	52.e	13.c	$3$	$2$	$1$	$0.415$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$-6$	$4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{3}-3q^{5}+4\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots$
52.2.f.a	$52$	$2$	52.f	52.f	$4$	$2$	$1$	$0.415$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$-6$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(1+i)q^{2}+2iq^{4}+(-3-3i)q^{5}+\cdots$
52.2.f.b	$52$	$2$	52.f	52.f	$4$	$8$	$4$	$0.415$	8.0.18939904.2	$_{}$	None	None		$4$	$0$	$-4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{2}-\beta _{5}+\beta _{7})q^{2}+(1-2\beta _{1}+\cdots)q^{3}+\cdots$
52.2.h.a	$52$	$2$	52.h	13.e	$6$	$2$	$1$	$0.415$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$1$	$0$	$-3$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\zeta_{6})q^{3}+(-2+\zeta_{6})q^{7}+2\zeta_{6}q^{9}+\cdots$
52.2.l.a	$52$	$2$	52.l	52.l	$12$	$4$	$1$	$0.415$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$6$	$0$		$1$	$\mathrm{U}(1)[D_{12}]$	$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots$
52.2.l.b	$52$	$2$	52.l	52.l	$12$	$16$	$4$	$0.415$	16.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$-2$	$0$	$-12$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	$q-\beta _{12}q^{2}+(\beta _{3}+\beta _{12}-\beta _{13}+\beta _{14}+\cdots)q^{3}+\cdots$
52.3.b.a	$52$	$3$	52.b	52.b	$2$	$1$	$1$	$1.417$	$\Q$	$_{}$	$\Q(\sqrt{-13}) $	None	✓	$2$	$0$	$-2$	$0$	$0$	$12$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+4q^{4}+12q^{7}-8q^{8}+9q^{9}+\cdots$
52.3.b.b	$52$	$3$	52.b	52.b	$2$	$1$	$1$	$1.417$	$\Q$	$_{}$	$\Q(\sqrt{-13}) $	None	✓	$2$	$0$	$2$	$0$	$0$	$-12$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+4q^{4}-12q^{7}+8q^{8}+9q^{9}+\cdots$
52.3.b.c	$52$	$3$	52.b	52.b	$2$	$2$	$2$	$1.417$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+iq^{2}-4q^{4}+4iq^{5}-4iq^{8}+9q^{9}+\cdots$
52.3.b.d	$52$	$3$	52.b	52.b	$2$	$8$	$8$	$1.417$	8.0.$\cdots$.3	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{6}q^{3}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{7})q^{5}+\cdots$
52.3.c.a	$52$	$3$	52.c	4.b	$2$	$12$	$12$	$1.417$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}-\beta _{2}q^{3}+\beta _{9}q^{4}+\beta _{8}q^{5}+\cdots$
52.3.g.a	$52$	$3$	52.g	13.d	$4$	$6$	$3$	$1.417$	6.0.$\cdots$.3	$_{}$	None	None		$2$	$0$	$0$	$0$	$-6$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{3}q^{3}+(-1+\beta _{2}-\beta _{5})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
52.3.i.a	$52$	$3$	52.i	52.i	$6$	$4$	$2$	$1.417$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{6}]$	$q+\zeta_{12}q^{2}+4\zeta_{12}^{2}q^{4}+(3-6\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
52.3.i.b	$52$	$3$	52.i	52.i	$6$	$20$	$10$	$1.417$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$4$	$0$	$-3$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{1}-\beta _{7})q^{2}+\beta _{11}q^{3}+(-1-\beta _{6}+\cdots)q^{4}+\cdots$
52.3.j.a	$52$	$3$	52.j	52.j	$6$	$24$	$12$	$1.417$		$_{}$	None	None		$4$	$0$	$-1$	$0$	$-12$	$0$			$\mathrm{SU}(2)[C_{6}]$
52.3.k.a	$52$	$3$	52.k	13.f	$12$	$8$	$2$	$1.417$	8.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$6$	$4$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(\beta _{1}-\beta _{4}+\beta _{5})q^{3}+(-\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots$
52.4.a.a	$52$	$4$	52.a	1.a	$1$	$1$	$1$	$3.068$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-3$	$-13$	$-11$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}-13q^{5}-11q^{7}-18q^{9}-2q^{11}+\cdots$
52.4.a.b	$52$	$4$	52.a	1.a	$1$	$2$	$2$	$3.068$	$\Q(\sqrt{217}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$23$	$27$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta )q^{3}+(11+\beta )q^{5}+(13+\beta )q^{7}+\cdots$
52.4.d.a	$52$	$4$	52.d	13.b	$2$	$2$	$2$	$3.068$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-8$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-4q^{3}-2\zeta_{6}q^{5}-9\zeta_{6}q^{7}-11q^{9}+\cdots$
52.4.d.b	$52$	$4$	52.d	13.b	$2$	$2$	$2$	$3.068$	$\Q(\sqrt{-433}) $	$_{}$	None	None		$2$	$0$	$0$	$14$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+7q^{3}+\beta q^{5}-\beta q^{7}+22q^{9}+(42+\cdots)q^{13}+\cdots$
52.4.e.a	$52$	$4$	52.e	13.c	$3$	$6$	$3$	$3.068$	6.0.6622206867.2	$_{}$	None	None		$2$	$0$	$0$	$0$	$-10$	$-16$		$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{5})q^{3}+(-2-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
52.4.f.a	$52$	$4$	52.f	52.f	$4$	$2$	$1$	$3.068$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-4$	$0$	$18$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-2-2i)q^{2}+8iq^{4}+(9+9i)q^{5}+\cdots$
52.4.f.b	$52$	$4$	52.f	52.f	$4$	$36$	$18$	$3.068$		$_{}$	None	None		$4$	$0$	$2$	$0$	$-20$	$0$			$\mathrm{SU}(2)[C_{4}]$
52.4.h.a	$52$	$4$	52.h	13.e	$6$	$8$	$4$	$3.068$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-36$		$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{5}q^{3}+(2-3\beta _{1}+\beta _{2}-\beta _{4})q^{5}+\cdots$
52.4.l.a	$52$	$4$	52.l	52.l	$12$	$4$	$1$	$3.068$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$4$	$0$	$-18$	$0$		$1$	$\mathrm{U}(1)[D_{12}]$	$q+(2\zeta_{12}+2\zeta_{12}^{2}-2\zeta_{12}^{3})q^{2}+8\zeta_{12}q^{4}+\cdots$
52.4.l.b	$52$	$4$	52.l	52.l	$12$	$72$	$18$	$3.068$		$_{}$	None	None		$4$	$0$	$-8$	$0$	$8$	$0$			$\mathrm{SU}(2)[C_{12}]$
52.5.b.a	$52$	$5$	52.b	52.b	$2$	$1$	$1$	$5.375$	$\Q$	$_{}$	$\Q(\sqrt{-13}) $	None	✓	$2$	$0$	$-4$	$0$	$0$	$-46$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-4q^{2}+2^{4}q^{4}-46q^{7}-2^{6}q^{8}+3^{4}q^{9}+\cdots$
52.5.b.b	$52$	$5$	52.b	52.b	$2$	$1$	$1$	$5.375$	$\Q$	$_{}$	$\Q(\sqrt{-13}) $	None	✓	$2$	$0$	$4$	$0$	$0$	$46$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{2}+2^{4}q^{4}+46q^{7}+2^{6}q^{8}+3^{4}q^{9}+\cdots$
52.5.b.c	$52$	$5$	52.b	52.b	$2$	$24$	$24$	$5.375$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
52.5.c.a	$52$	$5$	52.c	4.b	$2$	$24$	$24$	$5.375$		$_{}$	None	None		$2$	$0$	$6$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
52.5.g.a	$52$	$5$	52.g	13.d	$4$	$8$	$4$	$5.375$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-12$	$82$		$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{2}q^{3}+(-2-\beta _{3}+\beta _{5})q^{5}+(11+\cdots)q^{7}+\cdots$
52.5.i.a	$52$	$5$	52.i	52.i	$6$	$52$	$26$	$5.375$		$_{}$	None	None		$4$	$0$	$-3$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
52.5.j.a	$52$	$5$	52.j	52.j	$6$	$4$	$2$	$5.375$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$8$	$0$	$28$	$0$		$2^{6}\cdot 3^{2}$	$\mathrm{U}(1)[D_{6}]$	$q+(4-4\zeta_{12}^{2})q^{2}-2^{4}\zeta_{12}^{2}q^{4}+(7+\cdots)q^{5}+\cdots$
52.5.j.b	$52$	$5$	52.j	52.j	$6$	$48$	$24$	$5.375$		$_{}$	None	None		$4$	$0$	$-9$	$0$	$-12$	$0$			$\mathrm{SU}(2)[C_{6}]$
52.5.k.a	$52$	$5$	52.k	13.f	$12$	$20$	$5$	$5.375$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$12$	$28$		$2^{10}\cdot 3^{4}\cdot 13^{2}$	$\mathrm{SU}(2)[C_{12}]$	$q+(-\beta _{7}+\beta _{8})q^{3}+(-1-3\beta _{3}+2\beta _{5}+\cdots)q^{5}+\cdots$
52.6.a.a	$52$	$6$	52.a	1.a	$1$	$1$	$1$	$8.340$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-5$	$-3$	$53$	$+$	$1$	$\mathrm{SU}(2)$	$q-5q^{3}-3q^{5}+53q^{7}-218q^{9}-702q^{11}+\cdots$
52.6.a.b	$52$	$6$	52.a	1.a	$1$	$1$	$1$	$8.340$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$17$	$-91$	$-233$	$+$	$1$	$\mathrm{SU}(2)$	$q+17q^{3}-91q^{5}-233q^{7}+46q^{9}+\cdots$
52.6.a.c	$52$	$6$	52.a	1.a	$1$	$3$	$3$	$8.340$	3.3.203961.1	$_{}$	None	None	✓	$1$	$0$	$0$	$12$	$8$	$138$	$-$	$2$	$\mathrm{SU}(2)$	$q+(5+2\beta _{1}-\beta _{2})q^{3}+(6+5\beta _{1}-5\beta _{2})q^{5}+\cdots$
52.6.d.a	$52$	$6$	52.d	13.b	$2$	$6$	$6$	$8.340$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{3}+\beta _{1}q^{5}+\beta _{2}q^{7}+(118+\beta _{3}+\cdots)q^{9}+\cdots$
52.6.e.a	$52$	$6$	52.e	13.c	$3$	$12$	$6$	$8.340$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-9$	$-22$	$7$		$2^{12}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{1}+2\beta _{2})q^{3}+(-2+\beta _{3})q^{5}+(2+\cdots)q^{7}+\cdots$
52.6.f.a	$52$	$6$	52.f	52.f	$4$	$2$	$1$	$8.340$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-8$	$0$	$-6$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-4-4i)q^{2}+2^{5}iq^{4}+(-3-3i)q^{5}+\cdots$
52.6.f.b	$52$	$6$	52.f	52.f	$4$	$64$	$32$	$8.340$		$_{}$	None	None		$4$	$0$	$6$	$0$	$40$	$0$			$\mathrm{SU}(2)[C_{4}]$
52.6.h.a	$52$	$6$	52.h	13.e	$6$	$10$	$5$	$8.340$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$9$	$0$	$-87$		$2^{10}\cdot 3\cdot 13^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+(2\beta _{1}-\beta _{4})q^{3}+(-6+12\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
52.6.l.a	$52$	$6$	52.l	52.l	$12$	$4$	$1$	$8.340$	$\Q(\zeta_{12})$	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$8$	$0$	$6$	$0$		$1$	$\mathrm{U}(1)[D_{12}]$	$q+(4\zeta_{12}+4\zeta_{12}^{2}-4\zeta_{12}^{3})q^{2}+2^{5}\zeta_{12}q^{4}+\cdots$
52.6.l.b	$52$	$6$	52.l	52.l	$12$	$128$	$32$	$8.340$		$_{}$	None	None		$4$	$0$	$-12$	$0$	$-52$	$0$			$\mathrm{SU}(2)[C_{12}]$
52.7.b.a	$52$	$7$	52.b	52.b	$2$	$1$	$1$	$11.963$	$\Q$	$_{}$	$\Q(\sqrt{-13}) $	None	✓	$2$	$0$	$-8$	$0$	$0$	$-36$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-8q^{2}+2^{6}q^{4}-6^{2}q^{7}-2^{9}q^{8}+3^{6}q^{9}+\cdots$
52.7.b.b	$52$	$7$	52.b	52.b	$2$	$1$	$1$	$11.963$	$\Q$	$_{}$	$\Q(\sqrt{-13}) $	None	✓	$2$	$0$	$8$	$0$	$0$	$36$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+8q^{2}+2^{6}q^{4}+6^{2}q^{7}+2^{9}q^{8}+3^{6}q^{9}+\cdots$

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 163 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.