LMFDB - Newform orbit 630.4.a.k

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,4,Mod(1,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("630.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	630.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:	$37.1712033036$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$ q + 2 q^{2} + 4 q^{4} - 5 q^{5} - 7 q^{7} + 8 q^{8} - 10 q^{10} - 28 q^{11} + 54 q^{13} - 14 q^{14} + 16 q^{16} + 46 q^{17} + 12 q^{19} - 20 q^{20} - 56 q^{22} + 25 q^{25} + 108 q^{26} - 28 q^{28} - 6 q^{29}+ \cdots + 98 q^{98}+O(q^{100}) $

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

2.00000

4.00000

−5.00000

−7.00000

8.00000

−10.0000

Atkin-Lehner signs

$ p $	Sign
$2$	$ -1 $
$3$	$ -1 $
$5$	$ +1 $
$7$	$ +1 $

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	630.4.a.k		1
3.b	odd	2	1		210.4.a.f	✓	1
12.b	even	2	1		1680.4.a.h		1
15.d	odd	2	1		1050.4.a.p		1
15.e	even	4	2		1050.4.g.h		2
21.c	even	2	1		1470.4.a.d		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
210.4.a.f	✓	1	3.b	odd	2	1
630.4.a.k		1	1.a	even	1	1	trivial
1050.4.a.p		1	15.d	odd	2	1
1050.4.g.h		2	15.e	even	4	2
1470.4.a.d		1	21.c	even	2	1
1680.4.a.h		1	12.b	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(630))$:

$ T_{11} + 28 $

$ T_{13} - 54 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T - 2 $ T - 2
$3$	$ T $ T
$5$	$ T + 5 $ T + 5
$7$	$ T + 7 $ T + 7
$11$	$ T + 28 $ T + 28
$13$	$ T - 54 $ T - 54
$17$	$ T - 46 $ T - 46
$19$	$ T - 12 $ T - 12
$23$	$ T $ T
$29$	$ T + 6 $ T + 6
$31$	$ T - 296 $ T - 296
$37$	$ T - 134 $ T - 134
$41$	$ T + 146 $ T + 146
$43$	$ T - 556 $ T - 556
$47$	$ T - 448 $ T - 448
$53$	$ T + 46 $ T + 46
$59$	$ T + 748 $ T + 748
$61$	$ T + 50 $ T + 50
$67$	$ T + 156 $ T + 156
$71$	$ T - 1024 $ T - 1024
$73$	$ T + 310 $ T + 310
$79$	$ T - 856 $ T - 856
$83$	$ T - 628 $ T - 628
$89$	$ T - 590 $ T - 590
$97$	$ T + 1390 $ T + 1390
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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	630.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