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 113 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
954.2.a.a	$954$	$2$	954.a	1.a	$1$	$1$	$1$	$7.618$	$\Q$	None	✓				106.2.a.c	$1$	$1$	$-1$	$0$	$-3$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-3q^{5}+2q^{7}-q^{8}+3q^{10}+\cdots$
954.2.a.b	$954$	$2$	954.a	1.a	$1$	$1$	$1$	$7.618$	$\Q$	None	✓	✓			954.2.a.b	$1$	$0$	$-1$	$0$	$-2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-2q^{5}+4q^{7}-q^{8}+2q^{10}+\cdots$
954.2.a.c	$954$	$2$	954.a	1.a	$1$	$1$	$1$	$7.618$	$\Q$	None	✓				106.2.a.d	$1$	$1$	$-1$	$0$	$0$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-4q^{7}-q^{8}+5q^{13}+4q^{14}+\cdots$
954.2.a.d	$954$	$2$	954.a	1.a	$1$	$1$	$1$	$7.618$	$\Q$	None	✓				318.2.a.e	$1$	$1$	$-1$	$0$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+q^{7}-q^{8}-5q^{11}-q^{14}+\cdots$
954.2.a.e	$954$	$2$	954.a	1.a	$1$	$1$	$1$	$7.618$	$\Q$	None	✓	✓	✓	✓	954.2.a.e	$1$	$1$	$-1$	$0$	$2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+2q^{5}-3q^{7}-q^{8}-2q^{10}+\cdots$
954.2.a.f	$954$	$2$	954.a	1.a	$1$	$1$	$1$	$7.618$	$\Q$	None	✓				318.2.a.d	$1$	$0$	$-1$	$0$	$3$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}+3q^{5}-4q^{7}-q^{8}-3q^{10}+\cdots$
954.2.a.g	$954$	$2$	954.a	1.a	$1$	$1$	$1$	$7.618$	$\Q$	None	✓				318.2.a.b	$1$	$1$	$1$	$0$	$-4$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-4q^{5}+q^{7}+q^{8}-4q^{10}+\cdots$
954.2.a.h	$954$	$2$	954.a	1.a	$1$	$1$	$1$	$7.618$	$\Q$	None	✓	✓	✓	✓	954.2.a.e	$1$	$1$	$1$	$0$	$-2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-2q^{5}-3q^{7}+q^{8}-2q^{10}+\cdots$
954.2.a.i	$954$	$2$	954.a	1.a	$1$	$1$	$1$	$7.618$	$\Q$	None	✓				106.2.a.b	$1$	$1$	$1$	$0$	$-1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots$
954.2.a.j	$954$	$2$	954.a	1.a	$1$	$1$	$1$	$7.618$	$\Q$	None	✓				318.2.a.c	$1$	$0$	$1$	$0$	$0$	$5$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+5q^{7}+q^{8}+3q^{11}-4q^{13}+\cdots$
954.2.a.k	$954$	$2$	954.a	1.a	$1$	$1$	$1$	$7.618$	$\Q$	None	✓				318.2.a.a	$1$	$0$	$1$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+q^{11}+\cdots$
954.2.a.l	$954$	$2$	954.a	1.a	$1$	$1$	$1$	$7.618$	$\Q$	None	✓	✓			954.2.a.b	$1$	$0$	$1$	$0$	$2$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+2q^{5}+4q^{7}+q^{8}+2q^{10}+\cdots$
954.2.a.m	$954$	$2$	954.a	1.a	$1$	$1$	$1$	$7.618$	$\Q$	None	✓				106.2.a.a	$1$	$0$	$1$	$0$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+4q^{5}+q^{8}+4q^{10}+4q^{11}+\cdots$
954.2.a.n	$954$	$2$	954.a	1.a	$1$	$2$	$2$	$7.618$	$\Q(\sqrt{17}) $	None	✓		✓		318.2.a.g	$1$	$0$	$-2$	$0$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-\beta q^{5}+(1-\beta )q^{7}-q^{8}+\cdots$
954.2.a.o	$954$	$2$	954.a	1.a	$1$	$2$	$2$	$7.618$	$\Q(\sqrt{41}) $	None	✓		✓		318.2.a.f	$1$	$0$	$2$	$0$	$-1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}-\beta q^{5}+q^{8}-\beta q^{10}+(-2+\cdots)q^{11}+\cdots$
954.2.a.p	$954$	$2$	954.a	1.a	$1$	$3$	$3$	$7.618$	3.3.3132.1	None	✓	✓	✓		954.2.a.p	$1$	$0$	$-3$	$0$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{4}-\beta _{1}q^{5}+(-1-\beta _{1})q^{7}+\cdots$
954.2.a.q	$954$	$2$	954.a	1.a	$1$	$3$	$3$	$7.618$	3.3.3132.1	None	✓	✓	✓		954.2.a.p	$1$	$0$	$3$	$0$	$0$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+\beta _{1}q^{5}+(-1-\beta _{1})q^{7}+\cdots$
954.2.c.a	$954$	$2$	954.c	53.b	$2$	$2$	$2$	$7.618$	$\Q(\sqrt{-1}) $	None					106.2.b.a	$2$	$1$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+2 i q^{5}-2 q^{7}-i q^{8}+\cdots$
954.2.c.b	$954$	$2$	954.c	53.b	$2$	$2$	$2$	$7.618$	$\Q(\sqrt{-1}) $	None					318.2.c.b	$2$	$1$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}+3 i q^{5}-2 q^{7}+i q^{8}+\cdots$
954.2.c.c	$954$	$2$	954.c	53.b	$2$	$2$	$2$	$7.618$	$\Q(\sqrt{-1}) $	None					318.2.c.c	$2$	$0$	$0$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{2}-q^{4}+q^{7}-i q^{8}-3 q^{11}+\cdots$
954.2.c.d	$954$	$2$	954.c	53.b	$2$	$2$	$2$	$7.618$	$\Q(\sqrt{-1}) $	None					318.2.c.a	$2$	$0$	$0$	$0$	$0$	$2$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}+4 i q^{5}+q^{7}+i q^{8}+\cdots$
954.2.c.e	$954$	$2$	954.c	53.b	$2$	$2$	$2$	$7.618$	$\Q(\sqrt{-1}) $	None					106.2.b.b	$2$	$0$	$0$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{2}-q^{4}+i q^{5}+4 q^{7}+i q^{8}+\cdots$
954.2.c.f	$954$	$2$	954.c	53.b	$2$	$4$	$4$	$7.618$	$\Q(i, \sqrt{7})$	None		✓			954.2.c.f	$4$	$0$	$0$	$0$	$0$	$-8$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-q^{4}+\beta _{1}q^{5}-2q^{7}+\beta _{1}q^{8}+\cdots$
954.2.c.g	$954$	$2$	954.c	53.b	$2$	$4$	$4$	$7.618$	$\Q(i, \sqrt{17})$	None					318.2.c.d	$2$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}-q^{4}+(\beta _{1}-\beta _{2})q^{5}-2\beta _{3}q^{7}+\cdots$
954.2.c.h	$954$	$2$	954.c	53.b	$2$	$4$	$4$	$7.618$	$\Q(i, \sqrt{37})$	None		✓			954.2.c.h	$4$	$0$	$0$	$0$	$0$	$4$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}-q^{4}-2\beta _{1}q^{5}+q^{7}+\beta _{1}q^{8}+\cdots$
954.2.e.a	$954$	$2$	954.e	9.c	$3$	$2$	$1$	$7.618$	$\Q(\sqrt{-3}) $	None		✓			954.2.e.a	$2$	$1$	$1$	$0$	$-2$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
954.2.e.b	$954$	$2$	954.e	9.c	$3$	$2$	$1$	$7.618$	$\Q(\sqrt{-3}) $	None		✓			954.2.e.b	$2$	$0$	$1$	$3$	$2$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
954.2.e.c	$954$	$2$	954.e	9.c	$3$	$4$	$2$	$7.618$	$\Q(\sqrt{-3}, \sqrt{5})$	None		✓			954.2.e.c	$2$	$0$	$-2$	$6$	$1$	$6$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}+(1-\beta _{3})q^{3}+(-1-\beta _{3})q^{4}+\cdots$
954.2.e.d	$954$	$2$	954.e	9.c	$3$	$4$	$2$	$7.618$	$\Q(\sqrt{-3}, \sqrt{37})$	None		✓			954.2.e.d	$2$	$0$	$2$	$-6$	$-1$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\beta _{2})q^{2}+(-2+\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots$
954.2.e.e	$954$	$2$	954.e	9.c	$3$	$18$	$9$	$7.618$	$\mathbb{Q}[x]/(x^{18} - \cdots)$	None		✓			954.2.e.e	$2$	$0$	$-9$	$-4$	$7$	$0$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\beta _{7})q^{2}-\beta _{10}q^{3}-\beta _{7}q^{4}+\cdots$
954.2.e.f	$954$	$2$	954.e	9.c	$3$	$18$	$9$	$7.618$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	None		✓			954.2.e.f	$2$	$0$	$9$	$2$	$-7$	$4$		$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}-\beta _{7}q^{3}+(-1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$
954.2.e.g	$954$	$2$	954.e	9.c	$3$	$28$	$14$	$7.618$		None		✓			954.2.e.g	$2$	$0$	$-14$	$2$	$-6$	$-2$			$\mathrm{SU}(2)[C_{3}]$
954.2.e.h	$954$	$2$	954.e	9.c	$3$	$28$	$14$	$7.618$		None		✓			954.2.e.h	$2$	$0$	$14$	$-1$	$10$	$-1$			$\mathrm{SU}(2)[C_{3}]$
954.2.g.a	$954$	$2$	954.g	159.f	$4$	$4$	$2$	$7.618$	$\Q(\zeta_{8})$	None		✓			954.2.g.a	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(-1+2\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{5}+\cdots$
954.2.g.b	$954$	$2$	954.g	159.f	$4$	$4$	$2$	$7.618$	$\Q(\zeta_{8})$	None		✓			954.2.g.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(1+2\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{5}+\cdots$
954.2.g.c	$954$	$2$	954.g	159.f	$4$	$8$	$4$	$7.618$	8.0.959512576.1	None		✓			954.2.g.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{4}q^{2}+\beta _{2}q^{4}-\beta _{1}q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots$
954.2.g.d	$954$	$2$	954.g	159.f	$4$	$20$	$10$	$7.618$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None		✓	✓		954.2.g.d	$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{15}q^{2}+\beta _{7}q^{4}-\beta _{1}q^{5}+\beta _{9}q^{7}+\cdots$
954.2.i.a	$954$	$2$	954.i	477.i	$6$	$4$	$2$	$7.618$	$\Q(\zeta_{12})$	None		✓			954.2.i.a	$4$	$0$	$0$	$0$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(-2\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots$
954.2.i.b	$954$	$2$	954.i	477.i	$6$	$8$	$4$	$7.618$	8.0.592240896.1	None		✓			954.2.i.b	$4$	$0$	$0$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{2}q^{2}+(-\beta _{2}-\beta _{7})q^{3}+(1-\beta _{3}+\cdots)q^{4}+\cdots$
954.2.i.c	$954$	$2$	954.i	477.i	$6$	$8$	$4$	$7.618$	$\Q(\zeta_{24})$	None		✓			954.2.i.c	$4$	$0$	$0$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\zeta_{24}^{2}-\zeta_{24}^{6})q^{2}+(\zeta_{24}^{2}+\zeta_{24}^{6}+\cdots)q^{3}+\cdots$
954.2.i.d	$954$	$2$	954.i	477.i	$6$	$88$	$44$	$7.618$		None		✓	✓		954.2.i.d	$4$	$0$	$0$	$0$	$0$	$14$			$\mathrm{SU}(2)[C_{6}]$
954.2.k.a	$954$	$2$	954.k	477.k	$12$	$216$	$54$	$7.618$		None		✓	✓	✓	954.2.k.a	$4$	$0$	$0$	$-4$	$-12$	$0$			$\mathrm{SU}(2)[C_{12}]$
954.2.m.a	$954$	$2$	954.m	53.d	$13$	$12$	$1$	$7.618$	$\Q(\zeta_{26})$	None					318.2.g.a	$2$	$0$	$1$	$0$	$-5$	$7$		$1$	$\mathrm{SU}(2)[C_{13}]$	$q-\zeta_{26}^{10}q^{2}-\zeta_{26}^{7}q^{4}+(\zeta_{26}^{2}+\zeta_{26}^{6}+\cdots)q^{5}+\cdots$
954.2.m.b	$954$	$2$	954.m	53.d	$13$	$24$	$2$	$7.618$		None					106.2.d.a	$2$	$0$	$-2$	$0$	$-3$	$2$			$\mathrm{SU}(2)[C_{13}]$
954.2.m.c	$954$	$2$	954.m	53.d	$13$	$24$	$2$	$7.618$		None					318.2.g.c	$2$	$0$	$-2$	$0$	$3$	$-1$			$\mathrm{SU}(2)[C_{13}]$
954.2.m.d	$954$	$2$	954.m	53.d	$13$	$24$	$2$	$7.618$		None					318.2.g.b	$2$	$0$	$2$	$0$	$-3$	$3$			$\mathrm{SU}(2)[C_{13}]$
954.2.m.e	$954$	$2$	954.m	53.d	$13$	$36$	$3$	$7.618$		None					318.2.g.d	$2$	$0$	$-3$	$0$	$1$	$-5$			$\mathrm{SU}(2)[C_{13}]$
954.2.m.f	$954$	$2$	954.m	53.d	$13$	$36$	$3$	$7.618$		None					106.2.d.b	$2$	$0$	$3$	$0$	$9$	$-6$			$\mathrm{SU}(2)[C_{13}]$
954.2.m.g	$954$	$2$	954.m	53.d	$13$	$60$	$5$	$7.618$		None		✓			954.2.m.g	$2$	$0$	$-5$	$0$	$0$	$2$			$\mathrm{SU}(2)[C_{13}]$
954.2.m.h	$954$	$2$	954.m	53.d	$13$	$60$	$5$	$7.618$		None		✓			954.2.m.g	$2$	$0$	$5$	$0$	$0$	$2$			$\mathrm{SU}(2)[C_{13}]$

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 113 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.