LMFDB - Newform orbit 1152.4.a.l

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,4,Mod(1,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, 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("1152.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$N$	$=$	$1152 = 2^{7} \cdot 3^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	1152.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:	$67.9702003266$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 384)
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 + 8 q^{5} + 10 q^{7} + 68 q^{11} + 46 q^{13} + 74 q^{17} - 16 q^{19} - 20 q^{23} - 61 q^{25} + 228 q^{29} + 162 q^{31} + 80 q^{35} - 262 q^{37} - 30 q^{41} - 264 q^{43} + 124 q^{47} - 243 q^{49} - 204 q^{53}+ \cdots - 806 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

8.00000

10.0000

Atkin-Lehner signs

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

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	1152.4.a.l		1
3.b	odd	2	1		384.4.a.e	yes	1
4.b	odd	2	1		1152.4.a.k		1
8.b	even	2	1		1152.4.a.b		1
8.d	odd	2	1		1152.4.a.a		1
12.b	even	2	1		384.4.a.a	✓	1
24.f	even	2	1		384.4.a.h	yes	1
24.h	odd	2	1		384.4.a.d	yes	1
48.i	odd	4	2		768.4.d.e		2
48.k	even	4	2		768.4.d.l		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
384.4.a.a	✓	1	12.b	even	2	1
384.4.a.d	yes	1	24.h	odd	2	1
384.4.a.e	yes	1	3.b	odd	2	1
384.4.a.h	yes	1	24.f	even	2	1
768.4.d.e		2	48.i	odd	4	2
768.4.d.l		2	48.k	even	4	2
1152.4.a.a		1	8.d	odd	2	1
1152.4.a.b		1	8.b	even	2	1
1152.4.a.k		1	4.b	odd	2	1
1152.4.a.l		1	1.a	even	1	1	trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(1152))$ :

T_{5} - 8

T_{7} - 10

T_{13} - 46

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$ T
$3$	$T$ T
$5$	$T - 8$ T - 8
$7$	$T - 10$ T - 10
$11$	$T - 68$ T - 68
$13$	$T - 46$ T - 46
$17$	$T - 74$ T - 74
$19$	$T + 16$ T + 16
$23$	$T + 20$ T + 20
$29$	$T - 228$ T - 228
$31$	$T - 162$ T - 162
$37$	$T + 262$ T + 262
$41$	$T + 30$ T + 30
$43$	$T + 264$ T + 264
$47$	$T - 124$ T - 124
$53$	$T + 204$ T + 204
$59$	$T - 340$ T - 340
$61$	$T + 950$ T + 950
$67$	$T - 436$ T - 436
$71$	$T + 780$ T + 780
$73$	$T - 518$ T - 518
$79$	$T - 1010$ T - 1010
$83$	$T - 852$ T - 852
$89$	$T - 686$ T - 686
$97$	$T + 806$ T + 806
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