LMFDB - Newform orbit 432.5.e.a

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,5,Mod(161,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("432.161");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	432.e (of order $2$, degree $1$, not minimal)

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:	$44.6558240522$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$-1$

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} $

161.1

−71.0000

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	CM by $\Q(\sqrt{-3}) $

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	432.5.e.a		1
3.b	odd	2	1	CM	432.5.e.a		1
4.b	odd	2	1		27.5.b.a	✓	1
12.b	even	2	1		27.5.b.a	✓	1
20.d	odd	2	1		675.5.c.b		1
20.e	even	4	2		675.5.d.c		2
36.f	odd	6	2		81.5.d.a		2
36.h	even	6	2		81.5.d.a		2
60.h	even	2	1		675.5.c.b		1
60.l	odd	4	2		675.5.d.c		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
27.5.b.a	✓	1	4.b	odd	2	1
27.5.b.a	✓	1	12.b	even	2	1
81.5.d.a		2	36.f	odd	6	2
81.5.d.a		2	36.h	even	6	2
432.5.e.a		1	1.a	even	1	1	trivial
432.5.e.a		1	3.b	odd	2	1	CM
675.5.c.b		1	20.d	odd	2	1
675.5.c.b		1	60.h	even	2	1
675.5.d.c		2	20.e	even	4	2
675.5.d.c		2	60.l	odd	4	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{5}^{\mathrm{new}}(432, [\chi])$:

$ T_{5} $

$ T_{7} + 71 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T $ T
$5$	$ T $ T
$7$	$ T + 71 $ T + 71
$11$	$ T $ T
$13$	$ T + 337 $ T + 337
$17$	$ T $ T
$19$	$ T - 601 $ T - 601
$23$	$ T $ T
$29$	$ T $ T
$31$	$ T + 194 $ T + 194
$37$	$ T + 529 $ T + 529
$41$	$ T $ T
$43$	$ T - 3214 $ T - 3214
$47$	$ T $ T
$53$	$ T $ T
$59$	$ T $ T
$61$	$ T - 7199 $ T - 7199
$67$	$ T + 2903 $ T + 2903
$71$	$ T $ T
$73$	$ T + 1249 $ T + 1249
$79$	$ T + 4679 $ T + 4679
$83$	$ T $ T
$89$	$ T $ T
$97$	$ T - 9071 $ T - 9071
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Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	432.e (of order \(2\), degree \(1\), not minimal)

\(n\)	\(271\)	\(325\)	\(353\)
\(\chi(n)\)	\(1\)	\(1\)	\(-1\)

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