LMFDB - Newform orbit 4080.2.a.y

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4080,2,Mod(1,4080)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4080, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4080.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$4080 = 2^{4} \cdot 3 \cdot 5 \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	4080.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:	$32.5789640247$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 1020)
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 + q^{3} + q^{5} - 3 q^{7} + q^{9} - q^{11} - 2 q^{13} + q^{15} + q^{17} - q^{19} - 3 q^{21} - 6 q^{23} + q^{25} + q^{27} + 7 q^{29} + 10 q^{31} - q^{33} - 3 q^{35} - 3 q^{37} - 2 q^{39} - 9 q^{41}+ \cdots - 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

1.00000

−3.00000

1.00000

Atkin-Lehner signs

$p$	Sign
$2$	$-1$
$3$	$-1$
$5$	$-1$
$17$	$-1$

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	4080.2.a.y		1
4.b	odd	2	1		1020.2.a.d	✓	1
12.b	even	2	1		3060.2.a.f		1
20.d	odd	2	1		5100.2.a.m		1
20.e	even	4	2		5100.2.g.g		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1020.2.a.d	✓	1	4.b	odd	2	1
3060.2.a.f		1	12.b	even	2	1
4080.2.a.y		1	1.a	even	1	1	trivial
5100.2.a.m		1	20.d	odd	2	1
5100.2.g.g		2	20.e	even	4	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(4080))$ :

T_{7} + 3

T_{11} + 1

T_{13} + 2

T_{19} + 1

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$ T
$3$	$T - 1$ T - 1
$5$	$T - 1$ T - 1
$7$	$T + 3$ T + 3
$11$	$T + 1$ T + 1
$13$	$T + 2$ T + 2
$17$	$T - 1$ T - 1
$19$	$T + 1$ T + 1
$23$	$T + 6$ T + 6
$29$	$T - 7$ T - 7
$31$	$T - 10$ T - 10
$37$	$T + 3$ T + 3
$41$	$T + 9$ T + 9
$43$	$T + 8$ T + 8
$47$	$T + 3$ T + 3
$53$	$T - 5$ T - 5
$59$	$T + 8$ T + 8
$61$	$T - 10$ T - 10
$67$	$T + 16$ T + 16
$71$	$T + 12$ T + 12
$73$	$T + 9$ T + 9
$79$	$T + 2$ T + 2
$83$	$T + 12$ T + 12
$89$	$T$ T
$97$	$T + 2$ T + 2
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