LMFDB - Newform orbit 1089.2.a.f

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1089,2,Mod(1,1089)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1089, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1089.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$1089 = 3^{2} \cdot 11^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1089.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:	$8.69570878012$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$N(\mathrm{U}(1))$

$q$ -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^{4} + 5 q^{7} + 2 q^{13} + 4 q^{16} - 7 q^{19} - 5 q^{25} - 10 q^{28} + 11 q^{31} + 11 q^{37} + 8 q^{43} + 18 q^{49} - 4 q^{52} - q^{61} - 8 q^{64} + 11 q^{67} + 17 q^{73} + 14 q^{76} - 13 q^{79}+ \cdots + 5 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

5.00000

Atkin-Lehner signs

$p$	Sign
$3$	$+1$
$11$	$-1$

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	CM by $\Q(\sqrt{-3})$

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1089.2.a.f	yes	1
3.b	odd	2	1	CM	1089.2.a.f	yes	1
11.b	odd	2	1		1089.2.a.e	✓	1
33.d	even	2	1		1089.2.a.e	✓	1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1089.2.a.e	✓	1	11.b	odd	2	1
1089.2.a.e	✓	1	33.d	even	2	1
1089.2.a.f	yes	1	1.a	even	1	1	trivial
1089.2.a.f	yes	1	3.b	odd	2	1	CM

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(1089))$ :

T_{2}

T_{5}

T_{7} - 5

Hecke characteristic polynomials

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