LMFDB - Newform orbit 960.4.a.w

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:	$1$
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 + 3 q^{3} - 5 q^{5} - 4 q^{7} + 9 q^{9} - 40 q^{11} + 90 q^{13} - 15 q^{15} - 70 q^{17} - 40 q^{19} - 12 q^{21} + 108 q^{23} + 25 q^{25} + 27 q^{27} - 166 q^{29} - 40 q^{31} - 120 q^{33} + 20 q^{35}+ \cdots - 360 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

−4.00000

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.w		1
4.b	odd	2	1		960.4.a.f		1
8.b	even	2	1		480.4.a.d	✓	1
8.d	odd	2	1		480.4.a.k	yes	1
24.f	even	2	1		1440.4.a.f		1
24.h	odd	2	1		1440.4.a.e		1
40.e	odd	2	1		2400.4.a.d		1
40.f	even	2	1		2400.4.a.s		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
480.4.a.d	✓	1	8.b	even	2	1
480.4.a.k	yes	1	8.d	odd	2	1
960.4.a.f		1	4.b	odd	2	1
960.4.a.w		1	1.a	even	1	1	trivial
1440.4.a.e		1	24.h	odd	2	1
1440.4.a.f		1	24.f	even	2	1
2400.4.a.d		1	40.e	odd	2	1
2400.4.a.s		1	40.f	even	2	1

Hecke kernels

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

T_{7} + 4

T_{11} + 40

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$ T
$3$	$T - 3$ T - 3
$5$	$T + 5$ T + 5
$7$	$T + 4$ T + 4
$11$	$T + 40$ T + 40
$13$	$T - 90$ T - 90
$17$	$T + 70$ T + 70
$19$	$T + 40$ T + 40
$23$	$T - 108$ T - 108
$29$	$T + 166$ T + 166
$31$	$T + 40$ T + 40
$37$	$T - 130$ T - 130
$41$	$T + 310$ T + 310
$43$	$T - 268$ T - 268
$47$	$T + 556$ T + 556
$53$	$T - 370$ T - 370
$59$	$T + 240$ T + 240
$61$	$T - 130$ T - 130
$67$	$T + 876$ T + 876
$71$	$T + 840$ T + 840
$73$	$T - 250$ T - 250
$79$	$T + 880$ T + 880
$83$	$T - 188$ T - 188
$89$	$T + 726$ T + 726
$97$	$T + 1550$ T + 1550
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