LMFDB - Newform orbit 2535.2.a.f

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2535,2,Mod(1,2535)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2535, 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("2535.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$2535 = 3 \cdot 5 \cdot 13^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	2535.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:	$20.2420769124$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 195)
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^{3} - 2 q^{4} - q^{5} + 3 q^{7} + q^{9} - 3 q^{11} + 2 q^{12} + q^{15} + 4 q^{16} - 3 q^{17} + 2 q^{20} - 3 q^{21} + 3 q^{23} + q^{25} - q^{27} - 6 q^{28} - 6 q^{29} + 6 q^{31} + 3 q^{33} - 3 q^{35}+ \cdots - 3 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

−1.00000

−2.00000

−1.00000

3.00000

1.00000

Atkin-Lehner signs

$p$	Sign
$3$	$+1$
$5$	$+1$
$13$	$-1$

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	2535.2.a.f		1
3.b	odd	2	1		7605.2.a.n		1
13.b	even	2	1		2535.2.a.g		1
13.d	odd	4	2		195.2.b.a	✓	2
39.d	odd	2	1		7605.2.a.i		1
39.f	even	4	2		585.2.b.d		2
52.f	even	4	2		3120.2.g.j		2
65.f	even	4	2		975.2.h.c		2
65.g	odd	4	2		975.2.b.e		2
65.k	even	4	2		975.2.h.b		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
195.2.b.a	✓	2	13.d	odd	4	2
585.2.b.d		2	39.f	even	4	2
975.2.b.e		2	65.g	odd	4	2
975.2.h.b		2	65.k	even	4	2
975.2.h.c		2	65.f	even	4	2
2535.2.a.f		1	1.a	even	1	1	trivial
2535.2.a.g		1	13.b	even	2	1
3120.2.g.j		2	52.f	even	4	2
7605.2.a.i		1	39.d	odd	2	1
7605.2.a.n		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 $S_{2}^{\mathrm{new}}(\Gamma_0(2535))$ :

T_{2}

T_{7} - 3

T_{11} + 3

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$ T
$3$	$T + 1$ T + 1
$5$	$T + 1$ T + 1
$7$	$T - 3$ T - 3
$11$	$T + 3$ T + 3
$13$	$T$ T
$17$	$T + 3$ T + 3
$19$	$T$ T
$23$	$T - 3$ T - 3
$29$	$T + 6$ T + 6
$31$	$T - 6$ T - 6
$37$	$T + 9$ T + 9
$41$	$T + 3$ T + 3
$43$	$T - 10$ T - 10
$47$	$T + 12$ T + 12
$53$	$T + 3$ T + 3
$59$	$T - 12$ T - 12
$61$	$T - 1$ T - 1
$67$	$T$ T
$71$	$T - 9$ T - 9
$73$	$T - 6$ T - 6
$79$	$T - 1$ T - 1
$83$	$T - 6$ T - 6
$89$	$T - 15$ T - 15
$97$	$T - 9$ T - 9
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