LMFDB - Newform orbit 468.4.a.a

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [468,4,Mod(1,468)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(468, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("468.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$N$	$=$	$468 = 2^{2} \cdot 3^{2} \cdot 13$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	468.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:	$27.6128938827$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 156)
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^{5} - 32 q^{7} + 68 q^{11} + 13 q^{13} + 14 q^{17} + 4 q^{19} - 72 q^{23} - 121 q^{25} - 102 q^{29} - 136 q^{31} - 64 q^{35} - 386 q^{37} - 250 q^{41} - 140 q^{43} + 296 q^{47} + 681 q^{49} - 526 q^{53}+ \cdots - 446 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

−32.0000

Atkin-Lehner signs

$p$	Sign
$2$	$-1$
$3$	$-1$
$13$	$-1$

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	468.4.a.a		1
3.b	odd	2	1		156.4.a.b	✓	1
4.b	odd	2	1		1872.4.a.i		1
12.b	even	2	1		624.4.a.b		1
24.f	even	2	1		2496.4.a.m		1
24.h	odd	2	1		2496.4.a.d		1
39.d	odd	2	1		2028.4.a.b		1
39.f	even	4	2		2028.4.b.d		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
156.4.a.b	✓	1	3.b	odd	2	1
468.4.a.a		1	1.a	even	1	1	trivial
624.4.a.b		1	12.b	even	2	1
1872.4.a.i		1	4.b	odd	2	1
2028.4.a.b		1	39.d	odd	2	1
2028.4.b.d		2	39.f	even	4	2
2496.4.a.d		1	24.h	odd	2	1
2496.4.a.m		1	24.f	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{5} - 2$ T5 - 2 acting on $S_{4}^{\mathrm{new}}(\Gamma_0(468))$ .

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$ T
$3$	$T$ T
$5$	$T - 2$ T - 2
$7$	$T + 32$ T + 32
$11$	$T - 68$ T - 68
$13$	$T - 13$ T - 13
$17$	$T - 14$ T - 14
$19$	$T - 4$ T - 4
$23$	$T + 72$ T + 72
$29$	$T + 102$ T + 102
$31$	$T + 136$ T + 136
$37$	$T + 386$ T + 386
$41$	$T + 250$ T + 250
$43$	$T + 140$ T + 140
$47$	$T - 296$ T - 296
$53$	$T + 526$ T + 526
$59$	$T + 332$ T + 332
$61$	$T + 410$ T + 410
$67$	$T - 596$ T - 596
$71$	$T - 880$ T - 880
$73$	$T - 506$ T - 506
$79$	$T + 640$ T + 640
$83$	$T + 1380$ T + 1380
$89$	$T + 1450$ T + 1450
$97$	$T + 446$ T + 446
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