LMFDB - Newform orbit 960.4.a.v

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,4,Mod(1,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, 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("960.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$N$	$=$	$960 = 2^{6} \cdot 3 \cdot 5$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	960.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:	$56.6418336055$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 120)
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} - 5 q^{5} - 8 q^{7} + 9 q^{9} + 20 q^{11} - 22 q^{13} - 15 q^{15} - 14 q^{17} + 76 q^{19} - 24 q^{21} - 56 q^{23} + 25 q^{25} + 27 q^{27} + 154 q^{29} - 160 q^{31} + 60 q^{33} + 40 q^{35} + 162 q^{37}+ \cdots + 180 q^{99}+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

3.00000

−5.00000

−8.00000

9.00000

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	960.4.a.v		1
4.b	odd	2	1		960.4.a.g		1
8.b	even	2	1		240.4.a.d		1
8.d	odd	2	1		120.4.a.f	✓	1
24.f	even	2	1		360.4.a.e		1
24.h	odd	2	1		720.4.a.f		1
40.e	odd	2	1		600.4.a.d		1
40.f	even	2	1		1200.4.a.bf		1
40.i	odd	4	2		1200.4.f.g		2
40.k	even	4	2		600.4.f.g		2
120.m	even	2	1		1800.4.a.k		1
120.q	odd	4	2		1800.4.f.h		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
120.4.a.f	✓	1	8.d	odd	2	1
240.4.a.d		1	8.b	even	2	1
360.4.a.e		1	24.f	even	2	1
600.4.a.d		1	40.e	odd	2	1
600.4.f.g		2	40.k	even	4	2
720.4.a.f		1	24.h	odd	2	1
960.4.a.g		1	4.b	odd	2	1
960.4.a.v		1	1.a	even	1	1	trivial
1200.4.a.bf		1	40.f	even	2	1
1200.4.f.g		2	40.i	odd	4	2
1800.4.a.k		1	120.m	even	2	1
1800.4.f.h		2	120.q	odd	4	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(960))$ :

T_{7} + 8

T_{11} - 20

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$ T
$3$	$T - 3$ T - 3
$5$	$T + 5$ T + 5
$7$	$T + 8$ T + 8
$11$	$T - 20$ T - 20
$13$	$T + 22$ T + 22
$17$	$T + 14$ T + 14
$19$	$T - 76$ T - 76
$23$	$T + 56$ T + 56
$29$	$T - 154$ T - 154
$31$	$T + 160$ T + 160
$37$	$T - 162$ T - 162
$41$	$T + 390$ T + 390
$43$	$T - 388$ T - 388
$47$	$T - 544$ T - 544
$53$	$T - 210$ T - 210
$59$	$T + 380$ T + 380
$61$	$T - 794$ T - 794
$67$	$T + 148$ T + 148
$71$	$T - 840$ T - 840
$73$	$T - 858$ T - 858
$79$	$T + 144$ T + 144
$83$	$T - 316$ T - 316
$89$	$T - 1098$ T - 1098
$97$	$T - 994$ T - 994
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