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 9836 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
50021.2.a.a	$50021$	$2$	50021.a	1.a	$1$	$1998$	$1998$	$399.420$		None	✓	✓	✓	✓	50021.2.a.a	$1$		$-31$	$-97$	$-43$	$-169$	$+$		$\mathrm{SU}(2)$
50021.2.a.b	$50021$	$2$	50021.a	1.a	$1$	$2170$	$2170$	$399.420$		None	✓	✓	✓	✓	50021.2.a.b	$1$		$31$	$97$	$39$	$171$	$-$		$\mathrm{SU}(2)$
50023.2.a.a	$50023$	$2$	50023.a	1.a	$1$	$2029$	$2029$	$399.436$		None	✓	✓	✓	✓	50023.2.a.a	$1$		$-74$	$-119$	$-142$	$-77$	$+$		$\mathrm{SU}(2)$
50023.2.a.b	$50023$	$2$	50023.a	1.a	$1$	$2139$	$2139$	$399.436$		None	✓	✓	✓	✓	50023.2.a.b	$1$		$73$	$119$	$144$	$71$	$-$		$\mathrm{SU}(2)$
50033.2.a.a	$50033$	$2$	50033.a	1.a	$1$	$2050$	$2050$	$399.516$		None	✓	✓	✓	✓	50033.2.a.a	$1$		$-43$	$-113$	$-54$	$-373$	$+$		$\mathrm{SU}(2)$
50033.2.a.b	$50033$	$2$	50033.a	1.a	$1$	$2119$	$2119$	$399.516$		None	✓	✓	✓	✓	50033.2.a.b	$1$		$40$	$111$	$50$	$375$	$-$		$\mathrm{SU}(2)$
50047.2.a.a	$50047$	$2$	50047.a	1.a	$1$	$2037$	$2037$	$399.627$		None	✓	✓	✓	✓	50047.2.a.a	$1$		$-79$	$-109$	$-183$	$-70$	$+$		$\mathrm{SU}(2)$
50047.2.a.b	$50047$	$2$	50047.a	1.a	$1$	$2133$	$2133$	$399.627$		None	✓	✓	✓	✓	50047.2.a.b	$1$		$78$	$109$	$183$	$62$	$-$		$\mathrm{SU}(2)$
50051.2.a.a	$50051$	$2$	50051.a	1.a	$1$	$2013$	$2013$	$399.659$		None	✓	✓	✓	✓	50051.2.a.a	$1$		$-31$	$-70$	$-103$	$-125$	$+$		$\mathrm{SU}(2)$
50051.2.a.b	$50051$	$2$	50051.a	1.a	$1$	$2158$	$2158$	$399.659$		None	✓	✓	✓	✓	50051.2.a.b	$1$		$29$	$68$	$103$	$123$	$-$		$\mathrm{SU}(2)$
50053.2.a.a	$50053$	$2$	50053.a	1.a	$1$	$2064$	$2064$	$399.675$		None	✓	✓	✓	✓	50053.2.a.a	$1$		$-124$	$-167$	$-89$	$-103$	$+$		$\mathrm{SU}(2)$
50053.2.a.b	$50053$	$2$	50053.a	1.a	$1$	$2106$	$2106$	$399.675$		None	✓	✓	✓	✓	50053.2.a.b	$1$		$124$	$165$	$85$	$101$	$-$		$\mathrm{SU}(2)$
50069.2.a.a	$50069$	$2$	50069.a	1.a	$1$	$2006$	$2006$	$399.803$		None	✓	✓	✓	✓	50069.2.a.a	$1$		$-43$	$-104$	$-53$	$-122$	$+$		$\mathrm{SU}(2)$
50069.2.a.b	$50069$	$2$	50069.a	1.a	$1$	$2166$	$2166$	$399.803$		None	✓	✓	✓	✓	50069.2.a.b	$1$		$43$	$106$	$49$	$122$	$-$		$\mathrm{SU}(2)$
50077.2.a.a	$50077$	$2$	50077.a	1.a	$1$	$2058$	$2058$	$399.867$		None	✓	✓	✓	✓	50077.2.a.a	$1$		$-108$	$-129$	$-112$	$-138$	$+$		$\mathrm{SU}(2)$
50077.2.a.b	$50077$	$2$	50077.a	1.a	$1$	$2114$	$2114$	$399.867$		None	✓	✓	✓	✓	50077.2.a.b	$1$		$108$	$127$	$110$	$138$	$-$		$\mathrm{SU}(2)$
50087.2.a.a	$50087$	$2$	50087.a	1.a	$1$	$2025$	$2025$	$399.947$		None	✓	✓	✓	✓	50087.2.a.a	$1$		$-40$	$-68$	$-111$	$-260$	$+$		$\mathrm{SU}(2)$
50087.2.a.b	$50087$	$2$	50087.a	1.a	$1$	$2149$	$2149$	$399.947$		None	✓	✓	✓	✓	50087.2.a.b	$1$		$39$	$68$	$111$	$264$	$-$		$\mathrm{SU}(2)$
50093.2.a.a	$50093$	$2$	50093.a	1.a	$1$	$1$	$1$	$399.995$	$\Q$	None	✓	✓			50093.2.a.a	$1$		$2$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}-3q^{9}+q^{13}-4q^{16}+\cdots$
50093.2.a.b	$50093$	$2$	50093.a	1.a	$1$	$2045$	$2045$	$399.995$		None	✓	✓	✓	✓	50093.2.a.b	$1$		$-35$	$-246$	$-64$	$-169$	$+$		$\mathrm{SU}(2)$
50093.2.a.c	$50093$	$2$	50093.a	1.a	$1$	$2128$	$2128$	$399.995$		None	✓	✓	✓		50093.2.a.c	$1$		$31$	$248$	$62$	$167$	$-$		$\mathrm{SU}(2)$
50101.2.a.a	$50101$	$2$	50101.a	1.a	$1$	$2047$	$2047$	$400.058$		None	✓	✓	✓	✓	50101.2.a.a	$1$		$-56$	$-162$	$-115$	$-54$	$+$		$\mathrm{SU}(2)$
50101.2.a.b	$50101$	$2$	50101.a	1.a	$1$	$2127$	$2127$	$400.058$		None	✓	✓	✓	✓	50101.2.a.b	$1$		$54$	$162$	$111$	$50$	$-$		$\mathrm{SU}(2)$
50111.2.a.a	$50111$	$2$	50111.a	1.a	$1$	$1909$	$1909$	$400.138$		None	✓	✓	✓	✓	50111.2.a.a	$1$		$-32$	$-47$	$-87$	$-113$	$+$		$\mathrm{SU}(2)$
50111.2.a.b	$50111$	$2$	50111.a	1.a	$1$	$2267$	$2267$	$400.138$		None	✓	✓	✓	✓	50111.2.a.b	$1$		$33$	$49$	$91$	$119$	$-$		$\mathrm{SU}(2)$
50119.2.a.a	$50119$	$2$	50119.a	1.a	$1$	$2021$	$2021$	$400.202$		None	✓	✓	✓	✓	50119.2.a.a	$1$		$-65$	$-44$	$-125$	$-67$	$+$		$\mathrm{SU}(2)$
50119.2.a.b	$50119$	$2$	50119.a	1.a	$1$	$2155$	$2155$	$400.202$		None	✓	✓	✓	✓	50119.2.a.b	$1$		$66$	$42$	$125$	$61$	$-$		$\mathrm{SU}(2)$
50123.2.a.a	$50123$	$2$	50123.a	1.a	$1$	$2018$	$2018$	$400.234$		None	✓	✓	✓	✓	50123.2.a.a	$1$		$-52$	$-61$	$-126$	$-173$	$+$		$\mathrm{SU}(2)$
50123.2.a.b	$50123$	$2$	50123.a	1.a	$1$	$2159$	$2159$	$400.234$		None	✓	✓	✓	✓	50123.2.a.b	$1$		$52$	$61$	$126$	$173$	$-$		$\mathrm{SU}(2)$
50129.2.a.a	$50129$	$2$	50129.a	1.a	$1$	$2026$	$2026$	$400.282$		None	✓	✓	✓	✓	50129.2.a.a	$1$		$-23$	$-88$	$-63$	$-153$	$+$		$\mathrm{SU}(2)$
50129.2.a.b	$50129$	$2$	50129.a	1.a	$1$	$2151$	$2151$	$400.282$		None	✓	✓	✓	✓	50129.2.a.b	$1$		$20$	$88$	$59$	$155$	$-$		$\mathrm{SU}(2)$
50131.2.a.a	$50131$	$2$	50131.a	1.a	$1$	$2050$	$2050$	$400.298$		None	✓	✓	✓	✓	50131.2.a.a	$1$		$-64$	$-75$	$-159$	$-58$	$+$		$\mathrm{SU}(2)$
50131.2.a.b	$50131$	$2$	50131.a	1.a	$1$	$2127$	$2127$	$400.298$		None	✓	✓	✓	✓	50131.2.a.b	$1$		$62$	$71$	$159$	$54$	$-$		$\mathrm{SU}(2)$
50147.2.a.a	$50147$	$2$	50147.a	1.a	$1$	$1$	$1$	$400.426$	$\Q$	None	✓	✓			50147.2.a.a	$1$		$1$	$3$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+3q^{3}-q^{4}+3q^{6}-3q^{8}+6q^{9}+\cdots$
50147.2.a.b	$50147$	$2$	50147.a	1.a	$1$	$2020$	$2020$	$400.426$		None	✓	✓	✓		50147.2.a.b	$1$		$-67$	$-71$	$-91$	$-203$	$+$		$\mathrm{SU}(2)$
50147.2.a.c	$50147$	$2$	50147.a	1.a	$1$	$2158$	$2158$	$400.426$		None	✓	✓	✓	✓	50147.2.a.c	$1$		$66$	$66$	$89$	$203$	$-$		$\mathrm{SU}(2)$
50153.2.a.a	$50153$	$2$	50153.a	1.a	$1$	$2047$	$2047$	$400.474$		None	✓	✓	✓	✓	50153.2.a.a	$1$		$-57$	$-85$	$-49$	$-408$	$+$		$\mathrm{SU}(2)$
50153.2.a.b	$50153$	$2$	50153.a	1.a	$1$	$2132$	$2132$	$400.474$		None	✓	✓	✓	✓	50153.2.a.b	$1$		$56$	$83$	$47$	$414$	$-$		$\mathrm{SU}(2)$
50159.2.a.a	$50159$	$2$	50159.a	1.a	$1$	$1962$	$1962$	$400.522$		None	✓	✓	✓	✓	50159.2.a.a	$1$		$-35$	$-53$	$-91$	$-108$	$+$		$\mathrm{SU}(2)$
50159.2.a.b	$50159$	$2$	50159.a	1.a	$1$	$2218$	$2218$	$400.522$		None	✓	✓	✓	✓	50159.2.a.b	$1$		$34$	$55$	$95$	$112$	$-$		$\mathrm{SU}(2)$
50177.2.a.a	$50177$	$2$	50177.a	1.a	$1$	$1$	$1$	$400.665$	$\Q$	None	✓	✓			50177.2.a.a	$1$		$1$	$1$	$4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}+4q^{5}+q^{6}-3q^{8}+\cdots$
50177.2.a.b	$50177$	$2$	50177.a	1.a	$1$	$2054$	$2054$	$400.665$		None	✓	✓	✓		50177.2.a.b	$1$		$-35$	$-157$	$-73$	$-267$	$+$		$\mathrm{SU}(2)$
50177.2.a.c	$50177$	$2$	50177.a	1.a	$1$	$2126$	$2126$	$400.665$		None	✓	✓	✓	✓	50177.2.a.c	$1$		$31$	$156$	$67$	$269$	$-$		$\mathrm{SU}(2)$
50207.2.a.a	$50207$	$2$	50207.a	1.a	$1$	$1999$	$1999$	$400.905$		None	✓	✓	✓	✓	50207.2.a.a	$1$		$-58$	$-74$	$-52$	$-144$	$+$		$\mathrm{SU}(2)$
50207.2.a.b	$50207$	$2$	50207.a	1.a	$1$	$2185$	$2185$	$400.905$		None	✓	✓	✓	✓	50207.2.a.b	$1$		$59$	$74$	$50$	$148$	$-$		$\mathrm{SU}(2)$
50221.2.a.a	$50221$	$2$	50221.a	1.a	$1$	$1$	$1$	$401.017$	$\Q$	None	✓	✓			50221.2.a.a	$1$		$1$	$1$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-2q^{7}+\cdots$
50221.2.a.b	$50221$	$2$	50221.a	1.a	$1$	$2057$	$2057$	$401.017$		None	✓	✓	✓	✓	50221.2.a.b	$1$		$-67$	$-94$	$-127$	$-71$	$+$		$\mathrm{SU}(2)$
50221.2.a.c	$50221$	$2$	50221.a	1.a	$1$	$2126$	$2126$	$401.017$		None	✓	✓	✓		50221.2.a.c	$1$		$66$	$93$	$124$	$71$	$-$		$\mathrm{SU}(2)$
50227.2.a.a	$50227$	$2$	50227.a	1.a	$1$	$2068$	$2068$	$401.065$		None	✓	✓	✓	✓	50227.2.a.a	$1$		$-85$	$-59$	$-286$	$-105$	$+$		$\mathrm{SU}(2)$
50227.2.a.b	$50227$	$2$	50227.a	1.a	$1$	$2117$	$2117$	$401.065$		None	✓	✓	✓	✓	50227.2.a.b	$1$		$83$	$55$	$286$	$103$	$-$		$\mathrm{SU}(2)$

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 9836 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.