LMFDB - Newform orbit 2793.2.a.k

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2793,2,Mod(1,2793)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2793, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2793.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$2793 = 3 \cdot 7^{2} \cdot 19$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	2793.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:	$22.3022172845$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 399)
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} - q^{3} + 2 q^{4} - q^{5} - 2 q^{6} + q^{9} - 2 q^{10} + 4 q^{11} - 2 q^{12} - 4 q^{13} + q^{15} - 4 q^{16} - 3 q^{17} + 2 q^{18} + q^{19} - 2 q^{20} + 8 q^{22} - 3 q^{23} - 4 q^{25} - 8 q^{26}+ \cdots + 4 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

2.00000

−1.00000

2.00000

−1.00000

−2.00000

1.00000

−2.00000

Atkin-Lehner signs

$p$	Sign
$3$	$+1$
$7$	$-1$
$19$	$-1$

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	2793.2.a.k		1
3.b	odd	2	1		8379.2.a.c		1
7.b	odd	2	1		2793.2.a.l		1
7.d	odd	6	2		399.2.j.a	✓	2
21.c	even	2	1		8379.2.a.b		1
21.g	even	6	2		1197.2.j.b		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
399.2.j.a	✓	2	7.d	odd	6	2
1197.2.j.b		2	21.g	even	6	2
2793.2.a.k		1	1.a	even	1	1	trivial
2793.2.a.l		1	7.b	odd	2	1
8379.2.a.b		1	21.c	even	2	1
8379.2.a.c		1	3.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(2793))$ :

T_{2} - 2

T_{5} + 1

T_{11} - 4

T_{13} + 4

T_{17} + 3

Hecke characteristic polynomials

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