LMFDB - Newform orbit 7920.2.a.y

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7920,2,Mod(1,7920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7920, 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("7920.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$7920 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	7920.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:	$63.2415184009$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 660)
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^{5} - 2 q^{7} + q^{11} + 2 q^{13} - 2 q^{19} + q^{25} - 8 q^{31} - 2 q^{35} + 2 q^{37} - 2 q^{43} - 3 q^{49} - 6 q^{53} + q^{55} - 12 q^{59} + 2 q^{61} + 2 q^{65} + 4 q^{67} + 2 q^{73} - 2 q^{77}+ \cdots + 14 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

1.00000

−2.00000

Atkin-Lehner signs

$p$	Sign
$2$	$-1$
$3$	$-1$
$5$	$-1$
$11$	$-1$

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	7920.2.a.y		1
3.b	odd	2	1		2640.2.a.b		1
4.b	odd	2	1		1980.2.a.f		1
12.b	even	2	1		660.2.a.d	✓	1
20.d	odd	2	1		9900.2.a.e		1
20.e	even	4	2		9900.2.c.d		2
60.h	even	2	1		3300.2.a.b		1
60.l	odd	4	2		3300.2.c.i		2
132.d	odd	2	1		7260.2.a.l		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
660.2.a.d	✓	1	12.b	even	2	1
1980.2.a.f		1	4.b	odd	2	1
2640.2.a.b		1	3.b	odd	2	1
3300.2.a.b		1	60.h	even	2	1
3300.2.c.i		2	60.l	odd	4	2
7260.2.a.l		1	132.d	odd	2	1
7920.2.a.y		1	1.a	even	1	1	trivial
9900.2.a.e		1	20.d	odd	2	1
9900.2.c.d		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 $S_{2}^{\mathrm{new}}(\Gamma_0(7920))$ :

T_{7} + 2

T_{13} - 2

T_{17}

T_{19} + 2

T_{23}

T_{29}

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$ T
$3$	$T$ T
$5$	$T - 1$ T - 1
$7$	$T + 2$ T + 2
$11$	$T - 1$ T - 1
$13$	$T - 2$ T - 2
$17$	$T$ T
$19$	$T + 2$ T + 2
$23$	$T$ T
$29$	$T$ T
$31$	$T + 8$ T + 8
$37$	$T - 2$ T - 2
$41$	$T$ T
$43$	$T + 2$ T + 2
$47$	$T$ T
$53$	$T + 6$ T + 6
$59$	$T + 12$ T + 12
$61$	$T - 2$ T - 2
$67$	$T - 4$ T - 4
$71$	$T$ T
$73$	$T - 2$ T - 2
$79$	$T - 10$ T - 10
$83$	$T + 12$ T + 12
$89$	$T - 6$ T - 6
$97$	$T - 14$ T - 14
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