LMFDB - Newform orbit 441.8.a.d

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,8,Mod(1,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("441.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	441.a (trivial)

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:	$137.761796238$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Fricke sign:	$1$
Sato-Tate group:	$N(\mathrm{U}(1))$

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$ q - 128 q^{4}+O(q^{10}) $

$ q - 128 q^{4} + 2009 q^{13} + 16384 q^{16} + 14357 q^{19} - 78125 q^{25} - 331387 q^{31} + 335663 q^{37} - 409495 q^{43} - 257152 q^{52} - 3535546 q^{61} - 2097152 q^{64} + 4443527 q^{67} + 1236809 q^{73} - 1837696 q^{76} - 4517617 q^{79} + 12245198 q^{97}+O(q^{100}) $

Display 100 coefficients 10 coefficients

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} $

1.1

−128.000

Atkin-Lehner signs

$ p $	Sign
$3$	$1$
$7$	$1$

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	441.8.a.d		1
3.b	odd	2	1	CM	441.8.a.d		1
7.b	odd	2	1		441.8.a.c		1
7.c	even	3	2		63.8.e.a	✓	2
21.c	even	2	1		441.8.a.c		1
21.h	odd	6	2		63.8.e.a	✓	2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
63.8.e.a	✓	2	7.c	even	3	2
63.8.e.a	✓	2	21.h	odd	6	2
441.8.a.c		1	7.b	odd	2	1
441.8.a.c		1	21.c	even	2	1
441.8.a.d		1	1.a	even	1	1	trivial
441.8.a.d		1	3.b	odd	2	1	CM

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{8}^{\mathrm{new}}(\Gamma_0(441))$:

$ T_{2} $

$ T_{5} $

$ T_{13} - 2009 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T $ T
$5$	$ T $ T
$7$	$ T $ T
$11$	$ T $ T
$13$	$ T - 2009 $ T - 2009
$17$	$ T $ T
$19$	$ T - 14357 $ T - 14357
$23$	$ T $ T
$29$	$ T $ T
$31$	$ T + 331387 $ T + 331387
$37$	$ T - 335663 $ T - 335663
$41$	$ T $ T
$43$	$ T + 409495 $ T + 409495
$47$	$ T $ T
$53$	$ T $ T
$59$	$ T $ T
$61$	$ T + 3535546 $ T + 3535546
$67$	$ T - 4443527 $ T - 4443527
$71$	$ T $ T
$73$	$ T - 1236809 $ T - 1236809
$79$	$ T + 4517617 $ T + 4517617
$83$	$ T $ T
$89$	$ T $ T
$97$	$ T - 12245198 $ T - 12245198
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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	441.a (trivial)

\(n\):		e.g. 2-40 or 990-1000
Significant digits:
Format:

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more