LMFDB - Newform orbit 4864.2.a.a

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4864,2,Mod(1,4864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4864, 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("4864.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$4864 = 2^{8} \cdot 19$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	4864.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:	$38.8392355432$
Analytic rank:	$2$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 1216)
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 - 3 q^{3} - 4 q^{5} + q^{7} + 6 q^{9} - 5 q^{13} + 12 q^{15} - 5 q^{17} - q^{19} - 3 q^{21} - 3 q^{23} + 11 q^{25} - 9 q^{27} + 7 q^{29} - 10 q^{31} - 4 q^{35} - 2 q^{37} + 15 q^{39} + 6 q^{41} - 4 q^{43}+ \cdots - 12 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

−3.00000

−4.00000

1.00000

6.00000

Atkin-Lehner signs

$p$	Sign
$2$	$-1$
$19$	$+1$

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	4864.2.a.a		1
4.b	odd	2	1		4864.2.a.o		1
8.b	even	2	1		4864.2.a.p		1
8.d	odd	2	1		4864.2.a.b		1
16.e	even	4	2		1216.2.c.b	✓	2
16.f	odd	4	2		1216.2.c.c	yes	2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1216.2.c.b	✓	2	16.e	even	4	2
1216.2.c.c	yes	2	16.f	odd	4	2
4864.2.a.a		1	1.a	even	1	1	trivial
4864.2.a.b		1	8.d	odd	2	1
4864.2.a.o		1	4.b	odd	2	1
4864.2.a.p		1	8.b	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(4864))$ :

T_{3} + 3

T_{5} + 4

T_{7} - 1

T_{11}

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$ T
$3$	$T + 3$ T + 3
$5$	$T + 4$ T + 4
$7$	$T - 1$ T - 1
$11$	$T$ T
$13$	$T + 5$ T + 5
$17$	$T + 5$ T + 5
$19$	$T + 1$ T + 1
$23$	$T + 3$ T + 3
$29$	$T - 7$ T - 7
$31$	$T + 10$ T + 10
$37$	$T + 2$ T + 2
$41$	$T - 6$ T - 6
$43$	$T + 4$ T + 4
$47$	$T + 8$ T + 8
$53$	$T + 9$ T + 9
$59$	$T - 1$ T - 1
$61$	$T + 2$ T + 2
$67$	$T + 7$ T + 7
$71$	$T + 12$ T + 12
$73$	$T + 11$ T + 11
$79$	$T + 16$ T + 16
$83$	$T + 14$ T + 14
$89$	$T - 4$ T - 4
$97$	$T + 12$ T + 12
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