LMFDB - Newform orbit 2352.4.a.g

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2352,4,Mod(1,2352)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2352, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2352.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2352 = 2^{4} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2352.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:	$138.772492334$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 588)
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 - 3 q^{3} - 4 q^{5} + 9 q^{9}+O(q^{10}) $

$ q - 3 q^{3} - 4 q^{5} + 9 q^{9} + 20 q^{11} + 4 q^{13} + 12 q^{15} - 24 q^{17} + 44 q^{19} - 72 q^{23} - 109 q^{25} - 27 q^{27} - 38 q^{29} + 184 q^{31} - 60 q^{33} - 30 q^{37} - 12 q^{39} + 216 q^{41} + 164 q^{43} - 36 q^{45} + 520 q^{47} + 72 q^{51} - 146 q^{53} - 80 q^{55} - 132 q^{57} + 460 q^{59} - 628 q^{61} - 16 q^{65} - 556 q^{67} + 216 q^{69} - 592 q^{71} - 1024 q^{73} + 327 q^{75} + 104 q^{79} + 81 q^{81} - 324 q^{83} + 96 q^{85} + 114 q^{87} - 896 q^{89} - 552 q^{93} - 176 q^{95} + 920 q^{97} + 180 q^{99}+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

−3.00000

−4.00000

9.00000

Atkin-Lehner signs

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

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	2352.4.a.g		1
4.b	odd	2	1		588.4.a.e	yes	1
7.b	odd	2	1		2352.4.a.be		1
12.b	even	2	1		1764.4.a.i		1
28.d	even	2	1		588.4.a.b	✓	1
28.f	even	6	2		588.4.i.g		2
28.g	odd	6	2		588.4.i.b		2
84.h	odd	2	1		1764.4.a.d		1
84.j	odd	6	2		1764.4.k.j		2
84.n	even	6	2		1764.4.k.g		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
588.4.a.b	✓	1	28.d	even	2	1
588.4.a.e	yes	1	4.b	odd	2	1
588.4.i.b		2	28.g	odd	6	2
588.4.i.g		2	28.f	even	6	2
1764.4.a.d		1	84.h	odd	2	1
1764.4.a.i		1	12.b	even	2	1
1764.4.k.g		2	84.n	even	6	2
1764.4.k.j		2	84.j	odd	6	2
2352.4.a.g		1	1.a	even	1	1	trivial
2352.4.a.be		1	7.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(2352))$:

$ T_{5} + 4 $

$ T_{11} - 20 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T + 3 $ T + 3
$5$	$ T + 4 $ T + 4
$7$	$ T $ T
$11$	$ T - 20 $ T - 20
$13$	$ T - 4 $ T - 4
$17$	$ T + 24 $ T + 24
$19$	$ T - 44 $ T - 44
$23$	$ T + 72 $ T + 72
$29$	$ T + 38 $ T + 38
$31$	$ T - 184 $ T - 184
$37$	$ T + 30 $ T + 30
$41$	$ T - 216 $ T - 216
$43$	$ T - 164 $ T - 164
$47$	$ T - 520 $ T - 520
$53$	$ T + 146 $ T + 146
$59$	$ T - 460 $ T - 460
$61$	$ T + 628 $ T + 628
$67$	$ T + 556 $ T + 556
$71$	$ T + 592 $ T + 592
$73$	$ T + 1024 $ T + 1024
$79$	$ T - 104 $ T - 104
$83$	$ T + 324 $ T + 324
$89$	$ T + 896 $ T + 896
$97$	$ T - 920 $ T - 920
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:	\( N \)	\(=\)	\( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2352.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