LMFDB - Newform orbit 1083.1.b.b

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1083,1,Mod(362,1083)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1083, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 1, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1083.362");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1083 = 3 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1083.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$0.540487408682$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 57)
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.1083.1
Artin image:	$S_3$
Artin field:	Galois closure of 3.1.1083.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$

$=$

$ q + q^{3} + q^{4} - q^{7} + q^{9}+O(q^{10}) $

$ q + q^{3} + q^{4} - q^{7} + q^{9} + q^{12} - q^{13} + q^{16} - q^{21} + q^{25} + q^{27} - q^{28} - q^{31} + q^{36} - q^{37} - q^{39} - q^{43} + q^{48} - q^{52} - q^{61} - q^{63} + q^{64} - q^{67} - q^{73} + q^{75} - q^{79} + q^{81} - q^{84} + q^{91} - q^{93} + 2 q^{97}+O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1083\mathbb{Z}\right)^\times$.

$n$	$362$	$724$
$\chi(n)$	$-1$	$1$

Embeddings

For each embedding $\iota_m$ of the coefficient field, the values $\iota_m(a_n)$ are shown below.

For more information on an embedded modular form you can click on its label.

comment: embeddings in the coefficient field

gp: mfembed(f)

Label

$\iota_m(\nu)$

$ a_{2} $

$ a_{3} $

$ a_{4} $

$ a_{5} $

$ a_{6} $

$ a_{7} $

$ a_{8} $

$ a_{9} $

$ a_{10} $

362.1

1.00000

−1.00000

1.00000

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	CM by $\Q(\sqrt{-3}) $

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1083.1.b.b		1
3.b	odd	2	1	CM	1083.1.b.b		1
19.b	odd	2	1		1083.1.b.a		1
19.c	even	3	2		57.1.h.a	✓	2
19.d	odd	6	2		1083.1.h.a		2
19.e	even	9	6		1083.1.l.a		6
19.f	odd	18	6		1083.1.l.b		6
57.d	even	2	1		1083.1.b.a		1
57.f	even	6	2		1083.1.h.a		2
57.h	odd	6	2		57.1.h.a	✓	2
57.j	even	18	6		1083.1.l.b		6
57.l	odd	18	6		1083.1.l.a		6
76.g	odd	6	2		912.1.bl.a		2
95.i	even	6	2		1425.1.t.a		2
95.m	odd	12	4		1425.1.o.a		4
133.g	even	3	2		2793.1.bi.b		2
133.h	even	3	2		2793.1.n.a		2
133.k	odd	6	2		2793.1.bi.a		2
133.m	odd	6	2		2793.1.bf.a		2
133.t	odd	6	2		2793.1.n.b		2
152.k	odd	6	2		3648.1.bl.a		2
152.p	even	6	2		3648.1.bl.b		2
171.g	even	3	2		1539.1.n.a		2
171.h	even	3	2		1539.1.j.a		2
171.j	odd	6	2		1539.1.j.a		2
171.n	odd	6	2		1539.1.n.a		2
228.m	even	6	2		912.1.bl.a		2
285.n	odd	6	2		1425.1.t.a		2
285.v	even	12	4		1425.1.o.a		4
399.n	odd	6	2		2793.1.n.a		2
399.p	even	6	2		2793.1.n.b		2
399.z	even	6	2		2793.1.bf.a		2
399.bd	even	6	2		2793.1.bi.a		2
399.bi	odd	6	2		2793.1.bi.b		2
456.u	even	6	2		3648.1.bl.a		2
456.x	odd	6	2		3648.1.bl.b		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
57.1.h.a	✓	2	19.c	even	3	2
57.1.h.a	✓	2	57.h	odd	6	2
912.1.bl.a		2	76.g	odd	6	2
912.1.bl.a		2	228.m	even	6	2
1083.1.b.a		1	19.b	odd	2	1
1083.1.b.a		1	57.d	even	2	1
1083.1.b.b		1	1.a	even	1	1	trivial
1083.1.b.b		1	3.b	odd	2	1	CM
1083.1.h.a		2	19.d	odd	6	2
1083.1.h.a		2	57.f	even	6	2
1083.1.l.a		6	19.e	even	9	6
1083.1.l.a		6	57.l	odd	18	6
1083.1.l.b		6	19.f	odd	18	6
1083.1.l.b		6	57.j	even	18	6
1425.1.o.a		4	95.m	odd	12	4
1425.1.o.a		4	285.v	even	12	4
1425.1.t.a		2	95.i	even	6	2
1425.1.t.a		2	285.n	odd	6	2
1539.1.j.a		2	171.h	even	3	2
1539.1.j.a		2	171.j	odd	6	2
1539.1.n.a		2	171.g	even	3	2
1539.1.n.a		2	171.n	odd	6	2
2793.1.n.a		2	133.h	even	3	2
2793.1.n.a		2	399.n	odd	6	2
2793.1.n.b		2	133.t	odd	6	2
2793.1.n.b		2	399.p	even	6	2
2793.1.bf.a		2	133.m	odd	6	2
2793.1.bf.a		2	399.z	even	6	2
2793.1.bi.a		2	133.k	odd	6	2
2793.1.bi.a		2	399.bd	even	6	2
2793.1.bi.b		2	133.g	even	3	2
2793.1.bi.b		2	399.bi	odd	6	2
3648.1.bl.a		2	152.k	odd	6	2
3648.1.bl.a		2	456.u	even	6	2
3648.1.bl.b		2	152.p	even	6	2
3648.1.bl.b		2	456.x	odd	6	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{13} + 1 $ T13 + 1 acting on $S_{1}^{\mathrm{new}}(1083, [\chi])$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T - 1 $ T - 1
$5$	$ T $ T
$7$	$ T + 1 $ T + 1
$11$	$ T $ T
$13$	$ T + 1 $ T + 1
$17$	$ T $ T
$19$	$ T $ T
$23$	$ T $ T
$29$	$ T $ T
$31$	$ T + 1 $ T + 1
$37$	$ T + 1 $ T + 1
$41$	$ T $ T
$43$	$ T + 1 $ T + 1
$47$	$ T $ T
$53$	$ T $ T
$59$	$ T $ T
$61$	$ T + 1 $ T + 1
$67$	$ T + 1 $ T + 1
$71$	$ T $ T
$73$	$ T + 1 $ T + 1
$79$	$ T + 1 $ T + 1
$83$	$ T $ T
$89$	$ T $ T
$97$	$ T - 2 $ T - 2
show more
show less

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1083 = 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1083.b (of order \(2\), degree \(1\), minimal)

\(n\)	\(362\)	\(724\)
\(\chi(n)\)	\(-1\)	\(1\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more