LMFDB - Newform orbit 432.4.a.h

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,4,Mod(1,432)]

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, 0]))

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

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

chi := DirichletCharacter("432.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	432.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:	$25.4888251225$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 108)
Fricke sign:	$1$
Sato-Tate group:	$N(\mathrm{U}(1))$

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

37.0000

Atkin-Lehner signs

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

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	432.4.a.h		1
3.b	odd	2	1	CM	432.4.a.h		1
4.b	odd	2	1		108.4.a.b	✓	1
8.b	even	2	1		1728.4.a.r		1
8.d	odd	2	1		1728.4.a.o		1
12.b	even	2	1		108.4.a.b	✓	1
24.f	even	2	1		1728.4.a.o		1
24.h	odd	2	1		1728.4.a.r		1
36.f	odd	6	2		324.4.e.e		2
36.h	even	6	2		324.4.e.e		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
108.4.a.b	✓	1	4.b	odd	2	1
108.4.a.b	✓	1	12.b	even	2	1
324.4.e.e		2	36.f	odd	6	2
324.4.e.e		2	36.h	even	6	2
432.4.a.h		1	1.a	even	1	1	trivial
432.4.a.h		1	3.b	odd	2	1	CM
1728.4.a.o		1	8.d	odd	2	1
1728.4.a.o		1	24.f	even	2	1
1728.4.a.r		1	8.b	even	2	1
1728.4.a.r		1	24.h	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(432))$:

$ T_{5} $

$ T_{7} - 37 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T $ T
$5$	$ T $ T
$7$	$ T - 37 $ T - 37
$11$	$ T $ T
$13$	$ T + 19 $ T + 19
$17$	$ T $ T
$19$	$ T - 163 $ T - 163
$23$	$ T $ T
$29$	$ T $ T
$31$	$ T + 308 $ T + 308
$37$	$ T - 323 $ T - 323
$41$	$ T $ T
$43$	$ T - 520 $ T - 520
$47$	$ T $ T
$53$	$ T $ T
$59$	$ T $ T
$61$	$ T - 719 $ T - 719
$67$	$ T - 127 $ T - 127
$71$	$ T $ T
$73$	$ T + 919 $ T + 919
$79$	$ T - 1387 $ T - 1387
$83$	$ T $ T
$89$	$ T $ T
$97$	$ T + 523 $ T + 523
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Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	432.a (trivial)

\(n\):		e.g. 2-40 or 990-1000
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