LMFDB - Newform orbit 1089.2.a.d

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:	no (minimal twist has level 99)
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^{2} - q^{4} + 4 q^{5} + 2 q^{7} + 3 q^{8} - 4 q^{10} + 2 q^{13} - 2 q^{14} - q^{16} + 2 q^{17} + 6 q^{19} - 4 q^{20} - 4 q^{23} + 11 q^{25} - 2 q^{26} - 2 q^{28} - 6 q^{29} + 4 q^{31} - 5 q^{32}+ \cdots + 3 q^{98}+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

4.00000

2.00000

3.00000

−4.00000

Atkin-Lehner signs

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

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	1089.2.a.d		1
3.b	odd	2	1		1089.2.a.h		1
11.b	odd	2	1		99.2.a.c	yes	1
33.d	even	2	1		99.2.a.a	✓	1
44.c	even	2	1		1584.2.a.r		1
55.d	odd	2	1		2475.2.a.c		1
55.e	even	4	2		2475.2.c.g		2
77.b	even	2	1		4851.2.a.o		1
88.b	odd	2	1		6336.2.a.b		1
88.g	even	2	1		6336.2.a.f		1
99.g	even	6	2		891.2.e.j		2
99.h	odd	6	2		891.2.e.c		2
132.d	odd	2	1		1584.2.a.b		1
165.d	even	2	1		2475.2.a.j		1
165.l	odd	4	2		2475.2.c.b		2
231.h	odd	2	1		4851.2.a.g		1
264.m	even	2	1		6336.2.a.cl		1
264.p	odd	2	1		6336.2.a.cm		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
99.2.a.a	✓	1	33.d	even	2	1
99.2.a.c	yes	1	11.b	odd	2	1
891.2.e.c		2	99.h	odd	6	2
891.2.e.j		2	99.g	even	6	2
1089.2.a.d		1	1.a	even	1	1	trivial
1089.2.a.h		1	3.b	odd	2	1
1584.2.a.b		1	132.d	odd	2	1
1584.2.a.r		1	44.c	even	2	1
2475.2.a.c		1	55.d	odd	2	1
2475.2.a.j		1	165.d	even	2	1
2475.2.c.b		2	165.l	odd	4	2
2475.2.c.g		2	55.e	even	4	2
4851.2.a.g		1	231.h	odd	2	1
4851.2.a.o		1	77.b	even	2	1
6336.2.a.b		1	88.b	odd	2	1
6336.2.a.f		1	88.g	even	2	1
6336.2.a.cl		1	264.m	even	2	1
6336.2.a.cm		1	264.p	odd	2	1

Hecke kernels

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

T_{2} + 1

T_{5} - 4

T_{7} - 2

Hecke characteristic polynomials

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