LMFDB - Newform orbit 468.2.a.e

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [468,2,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, 2, names="a")

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

chi := DirichletCharacter("468.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 468 = 2^{2} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
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:	$3.73699881460$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
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

4.00000

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	468.2.a.e	yes	1
3.b	odd	2	1		468.2.a.a	✓	1
4.b	odd	2	1		1872.2.a.r		1
8.b	even	2	1		7488.2.a.f		1
8.d	odd	2	1		7488.2.a.a		1
9.c	even	3	2		4212.2.i.a		2
9.d	odd	6	2		4212.2.i.k		2
12.b	even	2	1		1872.2.a.a		1
13.b	even	2	1		6084.2.a.a		1
13.d	odd	4	2		6084.2.b.i		2
24.f	even	2	1		7488.2.a.ca		1
24.h	odd	2	1		7488.2.a.cd		1
39.d	odd	2	1		6084.2.a.p		1
39.f	even	4	2		6084.2.b.e		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
468.2.a.a	✓	1	3.b	odd	2	1
468.2.a.e	yes	1	1.a	even	1	1	trivial
1872.2.a.a		1	12.b	even	2	1
1872.2.a.r		1	4.b	odd	2	1
4212.2.i.a		2	9.c	even	3	2
4212.2.i.k		2	9.d	odd	6	2
6084.2.a.a		1	13.b	even	2	1
6084.2.a.p		1	39.d	odd	2	1
6084.2.b.e		2	39.f	even	4	2
6084.2.b.i		2	13.d	odd	4	2
7488.2.a.a		1	8.d	odd	2	1
7488.2.a.f		1	8.b	even	2	1
7488.2.a.ca		1	24.f	even	2	1
7488.2.a.cd		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 $S_{2}^{\mathrm{new}}(\Gamma_0(468))$:

$ T_{5} - 4 $

$ T_{7} - 4 $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T $ T
$5$	$ T - 4 $ T - 4
$7$	$ T - 4 $ T - 4
$11$	$ T + 4 $ T + 4
$13$	$ T + 1 $ T + 1
$17$	$ T $ T
$19$	$ T $ T
$23$	$ T + 8 $ T + 8
$29$	$ T + 8 $ T + 8
$31$	$ T - 4 $ T - 4
$37$	$ T - 6 $ T - 6
$41$	$ T - 12 $ T - 12
$43$	$ T + 8 $ T + 8
$47$	$ T + 4 $ T + 4
$53$	$ T $ T
$59$	$ T - 4 $ T - 4
$61$	$ T + 2 $ T + 2
$67$	$ T + 8 $ T + 8
$71$	$ T + 4 $ T + 4
$73$	$ T + 10 $ T + 10
$79$	$ T + 4 $ T + 4
$83$	$ T - 12 $ T - 12
$89$	$ T + 12 $ T + 12
$97$	$ T - 14 $ T - 14
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Level:	\( N \)	\(=\)	\( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	468.a (trivial)

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