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 83 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
116.1.d.a	$116$	$1$	116.d	116.d	$2$	$1$	$1$	$0.058$	$\Q$	$D_{3}$	$\Q(\sqrt{-29}) $	None	✓	$2$	$0$	$-1$	$1$	$-1$	$0$		$1$		$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
116.1.d.b	$116$	$1$	116.d	116.d	$2$	$1$	$1$	$0.058$	$\Q$	$D_{3}$	$\Q(\sqrt{-29}) $	None	✓	$2$	$0$	$1$	$-1$	$-1$	$0$		$1$		$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots$
116.1.j.a	$116$	$1$	116.j	116.j	$14$	$6$	$1$	$0.058$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$		$1$		$q-\zeta_{14}q^{2}+\zeta_{14}^{2}q^{4}+(\zeta_{14}^{4}-\zeta_{14}^{5}+\cdots)q^{5}+\cdots$
116.2.a.a	$116$	$2$	116.a	1.a	$1$	$1$	$1$	$0.926$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$3$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+3q^{5}+4q^{7}+6q^{9}-q^{11}+\cdots$
116.2.a.b	$116$	$2$	116.a	1.a	$1$	$1$	$1$	$0.926$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$3$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+3q^{5}-4q^{7}-2q^{9}+3q^{11}+\cdots$
116.2.a.c	$116$	$2$	116.a	1.a	$1$	$1$	$1$	$0.926$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}-2q^{5}+4q^{7}+q^{9}-6q^{11}+\cdots$
116.2.c.a	$116$	$2$	116.c	29.b	$2$	$2$	$2$	$0.926$	$\Q(\sqrt{-7}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$-4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{3}+q^{5}-2q^{7}-4q^{9}-\beta q^{11}+\cdots$
116.2.e.a	$116$	$2$	116.e	116.e	$4$	$2$	$1$	$0.926$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-1-i)q^{2}+2iq^{4}+4iq^{5}+(2+\cdots)q^{8}+\cdots$
116.2.e.b	$116$	$2$	116.e	116.e	$4$	$4$	$2$	$0.926$	$\Q(i, \sqrt{14})$	$_{}$	None	None		$4$	$0$	$-4$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}-2\beta _{2}q^{4}+\cdots$
116.2.e.c	$116$	$2$	116.e	116.e	$4$	$20$	$10$	$0.926$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$4$	$0$	$2$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{7}q^{2}+(\beta _{7}+\beta _{15})q^{3}+(-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
116.2.g.a	$116$	$2$	116.g	29.d	$7$	$6$	$1$	$0.926$	$\Q(\zeta_{14})$	$_{}$	None	None		$2$	$0$	$0$	$3$	$-3$	$3$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-1+2\zeta_{14}-2\zeta_{14}^{2}+2\zeta_{14}^{3}+\cdots)q^{3}+\cdots$
116.2.g.b	$116$	$2$	116.g	29.d	$7$	$12$	$2$	$0.926$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-3$	$-1$	$-7$		$1$	$\mathrm{SU}(2)[C_{7}]$	$q+(-\beta _{1}-\beta _{8})q^{3}+(-\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{5}+\cdots$
116.2.i.a	$116$	$2$	116.i	29.e	$14$	$6$	$1$	$0.926$	$\Q(\zeta_{14})$	$_{}$	None	None		$2$	$0$	$0$	$-7$	$-1$	$9$		$1$	$\mathrm{SU}(2)[C_{14}]$	$q+(-1-\zeta_{14}^{3})q^{3}+(-1-\zeta_{14}^{2}-2\zeta_{14}^{4}+\cdots)q^{5}+\cdots$
116.2.i.b	$116$	$2$	116.i	29.e	$14$	$6$	$1$	$0.926$	$\Q(\zeta_{14})$	$_{}$	None	None		$2$	$0$	$0$	$7$	$-1$	$-5$		$1$	$\mathrm{SU}(2)[C_{14}]$	$q+(1+\zeta_{14}^{3})q^{3}+(1-2\zeta_{14}+\zeta_{14}^{2}+\cdots)q^{5}+\cdots$
116.2.l.a	$116$	$2$	116.l	116.l	$28$	$12$	$1$	$0.926$	$\Q(\zeta_{28})$	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{28}]$	$q+(\zeta_{28}-\zeta_{28}^{8})q^{2}-2\zeta_{28}^{9}q^{4}+(1+\cdots)q^{5}+\cdots$
116.2.l.b	$116$	$2$	116.l	116.l	$28$	$144$	$12$	$0.926$		$_{}$	None	None		$4$	$0$	$-12$	$0$	$-28$	$0$			$\mathrm{SU}(2)[C_{28}]$
116.3.b.a	$116$	$3$	116.b	4.b	$2$	$28$	$28$	$3.161$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
116.3.d.a	$116$	$3$	116.d	116.d	$2$	$2$	$2$	$3.161$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-12$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+iq^{2}-4q^{4}-6q^{5}-4iq^{8}-9q^{9}+\cdots$
116.3.d.b	$116$	$3$	116.d	116.d	$2$	$3$	$3$	$3.161$	3.3.3132.1	$_{}$	$\Q(\sqrt{-29}) $	None	✓	$2$	$0$	$-6$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+(\beta _{1}+\beta _{2})q^{3}+4q^{4}+(\beta _{1}+2\beta _{2})q^{5}+\cdots$
116.3.d.c	$116$	$3$	116.d	116.d	$2$	$3$	$3$	$3.161$	3.3.3132.1	$_{}$	$\Q(\sqrt{-29}) $	None	✓	$2$	$0$	$6$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+(-\beta _{1}-\beta _{2})q^{3}+4q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
116.3.d.d	$116$	$3$	116.d	116.d	$2$	$20$	$20$	$3.161$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$12$	$0$		$2^{26}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-\beta _{6}q^{3}+(-1-\beta _{3})q^{4}+(1+\cdots)q^{5}+\cdots$
116.3.f.a	$116$	$3$	116.f	29.c	$4$	$10$	$5$	$3.161$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{3}+(-\beta _{3}+\beta _{5})q^{5}+\beta _{6}q^{7}+\cdots$
116.3.h.a	$116$	$3$	116.h	116.h	$14$	$12$	$2$	$3.161$	$\Q(\zeta_{28})$	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$12$	$0$		$2^{6}$	$\mathrm{U}(1)[D_{14}]$	$q-\zeta_{28}^{9}q^{2}-4\zeta_{28}^{4}q^{4}+(-2\zeta_{28}+\cdots)q^{5}+\cdots$
116.3.h.b	$116$	$3$	116.h	116.h	$14$	$156$	$26$	$3.161$		$_{}$	None	None		$4$	$0$	$-7$	$0$	$-26$	$0$			$\mathrm{SU}(2)[C_{14}]$
116.3.j.a	$116$	$3$	116.j	116.j	$14$	$168$	$28$	$3.161$		$_{}$	None	None		$4$	$0$	$-7$	$0$	$-14$	$0$			$\mathrm{SU}(2)[C_{14}]$
116.3.k.a	$116$	$3$	116.k	29.f	$28$	$60$	$5$	$3.161$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{28}]$
116.4.a.a	$116$	$4$	116.a	1.a	$1$	$2$	$2$	$6.844$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-10$	$-20$	$-$	$2$	$\mathrm{SU}(2)$	$q-\beta q^{3}+(-5+2\beta )q^{5}+(-10+4\beta )q^{7}+\cdots$
116.4.a.b	$116$	$4$	116.a	1.a	$1$	$2$	$2$	$6.844$	$\Q(\sqrt{22}) $	$_{}$	None	None	✓	$1$	$0$	$0$	$10$	$30$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+(5+\beta )q^{3}+15q^{5}-2\beta q^{7}+(20+10\beta )q^{9}+\cdots$
116.4.a.c	$116$	$4$	116.a	1.a	$1$	$3$	$3$	$6.844$	3.3.148344.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-10$	$-20$	$8$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-3-\beta _{1})q^{3}+(-7+\beta _{2})q^{5}+(4+\cdots)q^{7}+\cdots$
116.4.c.a	$116$	$4$	116.c	29.b	$2$	$8$	$8$	$6.844$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-22$	$12$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-3-\beta _{2})q^{5}+(1+\beta _{4})q^{7}+\cdots$
116.4.e.a	$116$	$4$	116.e	116.e	$4$	$2$	$1$	$6.844$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$4$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(2+2i)q^{2}+8iq^{4}+4iq^{5}+(-2^{4}+\cdots)q^{8}+\cdots$
116.4.e.b	$116$	$4$	116.e	116.e	$4$	$84$	$42$	$6.844$		$_{}$	None	None		$4$	$0$	$-4$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
116.4.g.a	$116$	$4$	116.g	29.d	$7$	$42$	$7$	$6.844$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$12$			$\mathrm{SU}(2)[C_{7}]$
116.4.i.a	$116$	$4$	116.i	29.e	$14$	$48$	$8$	$6.844$		$_{}$	None	None		$2$	$0$	$0$	$0$	$22$	$-12$			$\mathrm{SU}(2)[C_{14}]$
116.4.l.a	$116$	$4$	116.l	116.l	$28$	$12$	$1$	$6.844$	$\Q(\zeta_{28})$	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-4$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{28}]$	$q+(-2\zeta_{28}+2\zeta_{28}^{8})q^{2}-8\zeta_{28}^{9}q^{4}+\cdots$
116.4.l.b	$116$	$4$	116.l	116.l	$28$	$504$	$42$	$6.844$		$_{}$	None	None		$4$	$0$	$-10$	$0$	$-28$	$0$			$\mathrm{SU}(2)[C_{28}]$
116.5.b.a	$116$	$5$	116.b	4.b	$2$	$56$	$56$	$11.991$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
116.5.d.a	$116$	$5$	116.d	116.d	$2$	$3$	$3$	$11.991$	3.3.3132.1	$_{}$	$\Q(\sqrt{-29}) $	None	✓	$2$	$0$	$-12$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q-4q^{2}+(-2\beta _{1}+\beta _{2})q^{3}+2^{4}q^{4}+\cdots$
116.5.d.b	$116$	$5$	116.d	116.d	$2$	$3$	$3$	$11.991$	3.3.3132.1	$_{}$	$\Q(\sqrt{-29}) $	None	✓	$2$	$0$	$12$	$0$	$0$	$0$		$2^{2}$	$\mathrm{U}(1)[D_{2}]$	$q+4q^{2}+(2\beta _{1}-\beta _{2})q^{3}+2^{4}q^{4}+(3\beta _{1}+\cdots)q^{5}+\cdots$
116.5.d.c	$116$	$5$	116.d	116.d	$2$	$52$	$52$	$11.991$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-28$	$0$			$\mathrm{SU}(2)[C_{2}]$
116.5.f.a	$116$	$5$	116.f	29.c	$4$	$20$	$10$	$11.991$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{13}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{3}+(-2\beta _{2}-\beta _{10})q^{5}+(\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots$
116.5.h.a	$116$	$5$	116.h	116.h	$14$	$348$	$58$	$11.991$		$_{}$	None	None		$4$	$0$	$-7$	$0$	$14$	$0$			$\mathrm{SU}(2)[C_{14}]$
116.5.j.a	$116$	$5$	116.j	116.j	$14$	$12$	$2$	$11.991$	$\Q(\zeta_{28})$	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$8$	$0$	$28$	$0$		$2^{18}\cdot 3^{6}\cdot 7$	$\mathrm{U}(1)[D_{14}]$	$q+4\zeta_{28}q^{2}+2^{4}\zeta_{28}^{3}q^{4}+(\zeta_{28}^{2}-7\zeta_{28}^{6}+\cdots)q^{5}+\cdots$
116.5.j.b	$116$	$5$	116.j	116.j	$14$	$336$	$56$	$11.991$		$_{}$	None	None		$4$	$0$	$-7$	$0$	$-14$	$0$			$\mathrm{SU}(2)[C_{14}]$
116.5.k.a	$116$	$5$	116.k	29.f	$28$	$120$	$10$	$11.991$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{28}]$
116.6.a.a	$116$	$6$	116.a	1.a	$1$	$1$	$1$	$18.605$	$\Q$	$_{}$	None	None	✓	$1$	$2$	$0$	$-23$	$-67$	$-186$	$-$	$1$	$\mathrm{SU}(2)$	$q-23q^{3}-67q^{5}-186q^{7}+286q^{9}+\cdots$
116.6.a.b	$116$	$6$	116.a	1.a	$1$	$2$	$2$	$18.605$	$\Q(\sqrt{202}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$-22$	$-18$	$160$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-11+\beta )q^{3}-9q^{5}+(80-2\beta )q^{7}+\cdots$
116.6.a.c	$116$	$6$	116.a	1.a	$1$	$2$	$2$	$18.605$	$\Q(\sqrt{34}) $	$_{}$	None	None	✓	$1$	$1$	$0$	$34$	$-50$	$-208$	$+$	$1$	$\mathrm{SU}(2)$	$q+(17+\beta )q^{3}+(-5^{2}-12\beta )q^{5}+(-104+\cdots)q^{7}+\cdots$
116.6.a.d	$116$	$6$	116.a	1.a	$1$	$6$	$6$	$18.605$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	$_{}$	None	None	✓	$1$	$0$	$0$	$35$	$99$	$334$	$-$	$2^{6}$	$\mathrm{SU}(2)$	$q+(6-\beta _{1})q^{3}+(17+\beta _{2})q^{5}+(57-\beta _{1}+\cdots)q^{7}+\cdots$
116.6.c.a	$116$	$6$	116.c	29.b	$2$	$12$	$12$	$18.605$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-10$	$76$		$2^{20}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(-1-\beta _{4})q^{5}+(6+\beta _{3})q^{7}+\cdots$

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 83 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.