LMFDB - Newform orbit 882.4.a.e

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,4,Mod(1,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("882.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$N$	$=$	$882 = 2 \cdot 3^{2} \cdot 7^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	882.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:	$52.0396846251$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 126)
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 - 2 q^{2} + 4 q^{4} + 6 q^{5} - 8 q^{8} - 12 q^{10} - 30 q^{11} - 2 q^{13} + 16 q^{16} + 66 q^{17} + 52 q^{19} + 24 q^{20} + 60 q^{22} - 114 q^{23} - 89 q^{25} + 4 q^{26} - 72 q^{29} + 196 q^{31} - 32 q^{32}+ \cdots + 34 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

−2.00000

4.00000

6.00000

−8.00000

−12.0000

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	882.4.a.e		1
3.b	odd	2	1		882.4.a.m		1
7.b	odd	2	1		126.4.a.b	✓	1
7.c	even	3	2		882.4.g.q		2
7.d	odd	6	2		882.4.g.t		2
21.c	even	2	1		126.4.a.g	yes	1
21.g	even	6	2		882.4.g.e		2
21.h	odd	6	2		882.4.g.h		2
28.d	even	2	1		1008.4.a.g		1
84.h	odd	2	1		1008.4.a.n		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
126.4.a.b	✓	1	7.b	odd	2	1
126.4.a.g	yes	1	21.c	even	2	1
882.4.a.e		1	1.a	even	1	1	trivial
882.4.a.m		1	3.b	odd	2	1
882.4.g.e		2	21.g	even	6	2
882.4.g.h		2	21.h	odd	6	2
882.4.g.q		2	7.c	even	3	2
882.4.g.t		2	7.d	odd	6	2
1008.4.a.g		1	28.d	even	2	1
1008.4.a.n		1	84.h	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(882))$ :

T_{5} - 6

T_{11} + 30

T_{13} + 2

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T + 2$ T + 2
$3$	$T$ T
$5$	$T - 6$ T - 6
$7$	$T$ T
$11$	$T + 30$ T + 30
$13$	$T + 2$ T + 2
$17$	$T - 66$ T - 66
$19$	$T - 52$ T - 52
$23$	$T + 114$ T + 114
$29$	$T + 72$ T + 72
$31$	$T - 196$ T - 196
$37$	$T + 286$ T + 286
$41$	$T + 378$ T + 378
$43$	$T - 164$ T - 164
$47$	$T + 228$ T + 228
$53$	$T - 348$ T - 348
$59$	$T + 348$ T + 348
$61$	$T - 106$ T - 106
$67$	$T - 596$ T - 596
$71$	$T + 630$ T + 630
$73$	$T - 1042$ T - 1042
$79$	$T + 88$ T + 88
$83$	$T + 1440$ T + 1440
$89$	$T - 1374$ T - 1374
$97$	$T - 34$ T - 34
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