LMFDB - Newform orbit 1440.4.a.j

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1440,4,Mod(1,1440)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1440, 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("1440.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$N$	$=$	$1440 = 2^{5} \cdot 3^{2} \cdot 5$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	1440.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:	$84.9627504083$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 480)
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 - 5 q^{5} + 32 q^{7} - 64 q^{11} - 6 q^{13} - 38 q^{17} - 116 q^{19} + 120 q^{23} + 25 q^{25} + 122 q^{29} + 164 q^{31} - 160 q^{35} + 146 q^{37} + 238 q^{41} - 148 q^{43} + 184 q^{47} + 681 q^{49} - 470 q^{53}+ \cdots + 322 q^{97}+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

−5.00000

32.0000

Atkin-Lehner signs

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

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	1440.4.a.j		1
3.b	odd	2	1		480.4.a.l	yes	1
4.b	odd	2	1		1440.4.a.a		1
12.b	even	2	1		480.4.a.c	✓	1
15.d	odd	2	1		2400.4.a.a		1
24.f	even	2	1		960.4.a.t		1
24.h	odd	2	1		960.4.a.i		1
60.h	even	2	1		2400.4.a.v		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
480.4.a.c	✓	1	12.b	even	2	1
480.4.a.l	yes	1	3.b	odd	2	1
960.4.a.i		1	24.h	odd	2	1
960.4.a.t		1	24.f	even	2	1
1440.4.a.a		1	4.b	odd	2	1
1440.4.a.j		1	1.a	even	1	1	trivial
2400.4.a.a		1	15.d	odd	2	1
2400.4.a.v		1	60.h	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(1440))$ :

T_{7} - 32

T_{11} + 64

T_{17} + 38

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$ T
$3$	$T$ T
$5$	$T + 5$ T + 5
$7$	$T - 32$ T - 32
$11$	$T + 64$ T + 64
$13$	$T + 6$ T + 6
$17$	$T + 38$ T + 38
$19$	$T + 116$ T + 116
$23$	$T - 120$ T - 120
$29$	$T - 122$ T - 122
$31$	$T - 164$ T - 164
$37$	$T - 146$ T - 146
$41$	$T - 238$ T - 238
$43$	$T + 148$ T + 148
$47$	$T - 184$ T - 184
$53$	$T + 470$ T + 470
$59$	$T - 216$ T - 216
$61$	$T - 806$ T - 806
$67$	$T + 732$ T + 732
$71$	$T + 264$ T + 264
$73$	$T + 638$ T + 638
$79$	$T - 596$ T - 596
$83$	$T - 884$ T - 884
$89$	$T + 930$ T + 930
$97$	$T - 322$ T - 322
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