LMFDB - Newform orbit 2160.4.a.r

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2160,4,Mod(1,2160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2160, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2160.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2160 = 2^{4} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2160.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:	$127.444125612$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 270)
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)

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

5.00000

22.0000

Atkin-Lehner signs

$ p $	Sign
$2$	$ -1 $
$3$	$ +1 $
$5$	$ -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	2160.4.a.r		1
3.b	odd	2	1		2160.4.a.i		1
4.b	odd	2	1		270.4.a.c	✓	1
12.b	even	2	1		270.4.a.g	yes	1
20.d	odd	2	1		1350.4.a.z		1
20.e	even	4	2		1350.4.c.l		2
36.f	odd	6	2		810.4.e.s		2
36.h	even	6	2		810.4.e.k		2
60.h	even	2	1		1350.4.a.l		1
60.l	odd	4	2		1350.4.c.i		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
270.4.a.c	✓	1	4.b	odd	2	1
270.4.a.g	yes	1	12.b	even	2	1
810.4.e.k		2	36.h	even	6	2
810.4.e.s		2	36.f	odd	6	2
1350.4.a.l		1	60.h	even	2	1
1350.4.a.z		1	20.d	odd	2	1
1350.4.c.i		2	60.l	odd	4	2
1350.4.c.l		2	20.e	even	4	2
2160.4.a.i		1	3.b	odd	2	1
2160.4.a.r		1	1.a	even	1	1	trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(2160))$:

$ T_{7} - 22 $

$ T_{11} + 12 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T $ T
$5$	$ T - 5 $ T - 5
$7$	$ T - 22 $ T - 22
$11$	$ T + 12 $ T + 12
$13$	$ T - 38 $ T - 38
$17$	$ T - 105 $ T - 105
$19$	$ T - 157 $ T - 157
$23$	$ T + 117 $ T + 117
$29$	$ T + 66 $ T + 66
$31$	$ T - 25 $ T - 25
$37$	$ T - 314 $ T - 314
$41$	$ T - 504 $ T - 504
$43$	$ T + 380 $ T + 380
$47$	$ T + 252 $ T + 252
$53$	$ T + 3 $ T + 3
$59$	$ T + 318 $ T + 318
$61$	$ T - 293 $ T - 293
$67$	$ T - 322 $ T - 322
$71$	$ T + 120 $ T + 120
$73$	$ T - 44 $ T - 44
$79$	$ T + 917 $ T + 917
$83$	$ T - 309 $ T - 309
$89$	$ T + 1272 $ T + 1272
$97$	$ T - 1328 $ T - 1328
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Overview	Random
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Classical	Maass
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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2160.a (trivial)

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