LMFDB - Newform orbit 64.9.c.a

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,9,Mod(63,64)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("64.63");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	64.c (of order $2$, degree $1$, not 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:	$26.0722310439$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 4)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$1$	$-1$

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} $

63.1

1054.00

6561.00

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	64.9.c.a		1
4.b	odd	2	1	CM	64.9.c.a		1
8.b	even	2	1		4.9.b.a	✓	1
8.d	odd	2	1		4.9.b.a	✓	1
16.e	even	4	2		256.9.d.a		2
16.f	odd	4	2		256.9.d.a		2
24.f	even	2	1		36.9.d.a		1
24.h	odd	2	1		36.9.d.a		1
40.e	odd	2	1		100.9.b.a		1
40.f	even	2	1		100.9.b.a		1
40.i	odd	4	2		100.9.d.a		2
40.k	even	4	2		100.9.d.a		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
4.9.b.a	✓	1	8.b	even	2	1
4.9.b.a	✓	1	8.d	odd	2	1
36.9.d.a		1	24.f	even	2	1
36.9.d.a		1	24.h	odd	2	1
64.9.c.a		1	1.a	even	1	1	trivial
64.9.c.a		1	4.b	odd	2	1	CM
100.9.b.a		1	40.e	odd	2	1
100.9.b.a		1	40.f	even	2	1
100.9.d.a		2	40.i	odd	4	2
100.9.d.a		2	40.k	even	4	2
256.9.d.a		2	16.e	even	4	2
256.9.d.a		2	16.f	odd	4	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{3} $ T3 acting on $S_{9}^{\mathrm{new}}(64, [\chi])$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T $ T
$5$	$ T - 1054 $ T - 1054
$7$	$ T $ T
$11$	$ T $ T
$13$	$ T - 478 $ T - 478
$17$	$ T + 63358 $ T + 63358
$19$	$ T $ T
$23$	$ T $ T
$29$	$ T - 1407838 $ T - 1407838
$31$	$ T $ T
$37$	$ T + 925922 $ T + 925922
$41$	$ T - 3577922 $ T - 3577922
$43$	$ T $ T
$47$	$ T $ T
$53$	$ T - 9620638 $ T - 9620638
$59$	$ T $ T
$61$	$ T + 20722082 $ T + 20722082
$67$	$ T $ T
$71$	$ T $ T
$73$	$ T + 54717118 $ T + 54717118
$79$	$ T $ T
$83$	$ T $ T
$89$	$ T + 30265918 $ T + 30265918
$97$	$ T + 173379838 $ T + 173379838
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:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	64.c (of order \(2\), degree \(1\), not minimal)

\(n\)	\(5\)	\(63\)
\(\chi(n)\)	\(1\)	\(-1\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more