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 66 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
4200.2.a.a	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	✓			4200.2.a.a	$1$	$1$	$0$	$-1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-3q^{11}-2q^{13}+\cdots$
4200.2.a.b	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	✓			4200.2.a.b	$1$	$1$	$0$	$-1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-q^{11}+4q^{13}+2q^{17}+\cdots$
4200.2.a.c	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓				840.2.a.i	$1$	$1$	$0$	$-1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}-2q^{13}-2q^{17}+\cdots$
4200.2.a.d	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	✓			4200.2.a.d	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-5q^{11}-4q^{13}+\cdots$
4200.2.a.e	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓				840.2.a.g	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots$
4200.2.a.f	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	✓			4200.2.a.f	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-3q^{11}-2q^{13}+\cdots$
4200.2.a.g	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	✓			4200.2.a.g	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-2q^{11}-5q^{13}+\cdots$
4200.2.a.h	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓				840.2.a.h	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-6q^{13}+2q^{17}+\cdots$
4200.2.a.i	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓				168.2.a.b	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+2q^{13}-6q^{17}+\cdots$
4200.2.a.j	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓				840.2.t.b	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots$
4200.2.a.k	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓				840.2.t.a	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots$
4200.2.a.l	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	✓			4200.2.a.l	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+2q^{11}+3q^{13}+\cdots$
4200.2.a.m	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	✓			4200.2.a.m	$1$	$1$	$0$	$-1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+3q^{11}+2q^{17}+\cdots$
4200.2.a.n	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓				840.2.a.j	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
4200.2.a.o	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	✓			4200.2.a.o	$1$	$0$	$0$	$-1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}+5q^{11}+2q^{13}+\cdots$
4200.2.a.p	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	✓			4200.2.a.d	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-5q^{11}+4q^{13}+\cdots$
4200.2.a.q	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓				840.2.a.b	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots$
4200.2.a.r	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	✓			4200.2.a.f	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-3q^{11}+2q^{13}+\cdots$
4200.2.a.s	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	✓			4200.2.a.g	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-2q^{11}+5q^{13}+\cdots$
4200.2.a.t	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓				168.2.a.a	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-6q^{13}+2q^{17}+\cdots$
4200.2.a.u	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓				840.2.a.c	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+2q^{13}-6q^{17}+\cdots$
4200.2.a.v	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	✓			4200.2.a.l	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+2q^{11}-3q^{13}+\cdots$
4200.2.a.w	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓				840.2.t.b	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots$
4200.2.a.x	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓				840.2.t.a	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots$
4200.2.a.y	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	✓			4200.2.a.m	$1$	$1$	$0$	$1$	$0$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+3q^{11}-2q^{17}+\cdots$
4200.2.a.z	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓				840.2.a.f	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
4200.2.a.ba	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	✓			4200.2.a.o	$1$	$0$	$0$	$1$	$0$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}+5q^{11}-2q^{13}+\cdots$
4200.2.a.bb	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓				840.2.a.d	$1$	$1$	$0$	$1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
4200.2.a.bc	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	✓			4200.2.a.a	$1$	$1$	$0$	$1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}-3q^{11}+2q^{13}+\cdots$
4200.2.a.bd	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓	✓			4200.2.a.b	$1$	$1$	$0$	$1$	$0$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}-q^{11}-4q^{13}-2q^{17}+\cdots$
4200.2.a.be	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓				840.2.a.e	$1$	$0$	$0$	$1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}-2q^{13}-2q^{17}+\cdots$
4200.2.a.bf	$4200$	$2$	4200.a	1.a	$1$	$1$	$1$	$33.537$	$\Q$	None	✓				840.2.a.a	$1$	$0$	$0$	$1$	$0$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
4200.2.a.bg	$4200$	$2$	4200.a	1.a	$1$	$2$	$2$	$33.537$	$\Q(\sqrt{2}) $	None	✓				840.2.a.k	$1$	$0$	$0$	$-2$	$0$	$-2$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+\beta q^{11}-2q^{13}+\cdots$
4200.2.a.bh	$4200$	$2$	4200.a	1.a	$1$	$2$	$2$	$33.537$	$\Q(\sqrt{73}) $	None	✓	✓			4200.2.a.bh	$1$	$0$	$0$	$-2$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+\beta q^{11}+(-1-\beta )q^{13}+\cdots$
4200.2.a.bi	$4200$	$2$	4200.a	1.a	$1$	$2$	$2$	$33.537$	$\Q(\sqrt{17}) $	None	✓	✓			4200.2.a.bi	$1$	$0$	$0$	$-2$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+(1+\beta )q^{11}+(-2+\cdots)q^{13}+\cdots$
4200.2.a.bj	$4200$	$2$	4200.a	1.a	$1$	$2$	$2$	$33.537$	$\Q(\sqrt{5}) $	None	✓		✓		840.2.t.c	$1$	$0$	$0$	$-2$	$0$	$2$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}+q^{7}+q^{9}-2q^{11}-\beta q^{13}+\cdots$
4200.2.a.bk	$4200$	$2$	4200.a	1.a	$1$	$2$	$2$	$33.537$	$\Q(\sqrt{5}) $	None	✓		✓		840.2.t.c	$1$	$1$	$0$	$2$	$0$	$-2$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}-q^{7}+q^{9}-2q^{11}+\beta q^{13}+\cdots$
4200.2.a.bl	$4200$	$2$	4200.a	1.a	$1$	$2$	$2$	$33.537$	$\Q(\sqrt{73}) $	None	✓	✓	✓		4200.2.a.bh	$1$	$0$	$0$	$2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}+\beta q^{11}+(1+\beta )q^{13}+\cdots$
4200.2.a.bm	$4200$	$2$	4200.a	1.a	$1$	$2$	$2$	$33.537$	$\Q(\sqrt{17}) $	None	✓	✓			4200.2.a.bi	$1$	$0$	$0$	$2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}+(1+\beta )q^{11}+(2-3\beta )q^{13}+\cdots$
4200.2.a.bn	$4200$	$2$	4200.a	1.a	$1$	$3$	$3$	$33.537$	3.3.148.1	None	✓		✓		840.2.t.d	$1$	$0$	$0$	$-3$	$0$	$-3$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+(-1-\beta _{1}+\beta _{2})q^{11}+\cdots$
4200.2.a.bo	$4200$	$2$	4200.a	1.a	$1$	$3$	$3$	$33.537$	3.3.148.1	None	✓		✓		840.2.t.e	$1$	$1$	$0$	$-3$	$0$	$-3$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{3}-q^{7}+q^{9}+(1+\beta _{1}+\beta _{2})q^{11}+\cdots$
4200.2.a.bp	$4200$	$2$	4200.a	1.a	$1$	$3$	$3$	$33.537$	3.3.148.1	None	✓		✓		840.2.t.d	$1$	$1$	$0$	$3$	$0$	$3$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}+(-1-\beta _{1}+\beta _{2})q^{11}+\cdots$
4200.2.a.bq	$4200$	$2$	4200.a	1.a	$1$	$3$	$3$	$33.537$	3.3.148.1	None	✓		✓		840.2.t.e	$1$	$0$	$0$	$3$	$0$	$3$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{3}+q^{7}+q^{9}+(1+\beta _{1}+\beta _{2})q^{11}+\cdots$
4200.2.t.a	$4200$	$2$	4200.t	5.b	$2$	$2$	$2$	$33.537$	$\Q(\sqrt{-1}) $	None		✓			4200.2.a.d	$2$	$1$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}-i q^{7}-q^{9}-5 q^{11}-4 i q^{13}+\cdots$
4200.2.t.b	$4200$	$2$	4200.t	5.b	$2$	$2$	$2$	$33.537$	$\Q(\sqrt{-1}) $	None					840.2.a.b	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}-i q^{7}-q^{9}-4 q^{11}+2 i q^{13}+\cdots$
4200.2.t.c	$4200$	$2$	4200.t	5.b	$2$	$2$	$2$	$33.537$	$\Q(\sqrt{-1}) $	None					840.2.a.d	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}+i q^{7}-q^{9}-4 q^{11}-2 i q^{13}+\cdots$
4200.2.t.d	$4200$	$2$	4200.t	5.b	$2$	$2$	$2$	$33.537$	$\Q(\sqrt{-1}) $	None					840.2.a.g	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}-i q^{7}-q^{9}-4 q^{11}+6 i q^{13}+\cdots$
4200.2.t.e	$4200$	$2$	4200.t	5.b	$2$	$2$	$2$	$33.537$	$\Q(\sqrt{-1}) $	None		✓			4200.2.a.f	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-i q^{3}-i q^{7}-q^{9}-3 q^{11}-2 i q^{13}+\cdots$
4200.2.t.f	$4200$	$2$	4200.t	5.b	$2$	$2$	$2$	$33.537$	$\Q(\sqrt{-1}) $	None		✓			4200.2.a.a	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}-i q^{7}-q^{9}-3 q^{11}+2 i q^{13}+\cdots$
4200.2.t.g	$4200$	$2$	4200.t	5.b	$2$	$2$	$2$	$33.537$	$\Q(\sqrt{-1}) $	None		✓			4200.2.a.g	$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+i q^{7}-q^{9}-2 q^{11}+5 i q^{13}+\cdots$

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Learn more

Refine search

Results (1-50 of 66 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.