LMFDB - Newform orbit 2176.1.e.a

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2176,1,Mod(1087,2176)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2176, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("2176.1087");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2176 = 2^{7} \cdot 17 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2176.e (of order $2$, degree $1$, 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:	$1.08596546749$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{2}$
Projective field:	Galois closure of $\Q(i, \sqrt{34})$
Artin image:	$D_4$
Artin field:	Galois closure of 4.0.8704.2

$q$-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 $\left(\mathbb{Z}/2176\mathbb{Z}\right)^\times$.

$n$	$511$	$513$	$1157$
$\chi(n)$	$-1$	$-1$	$-1$

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} $

1087.1

−2.00000

1.00000

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	CM by $\Q(\sqrt{-1}) $
136.e	odd	2	1	CM by $\Q(\sqrt{-34}) $
136.h	even	2	1	RM by $\Q(\sqrt{34}) $

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2176.1.e.a	✓	1
4.b	odd	2	1	CM	2176.1.e.a	✓	1
8.b	even	2	1		2176.1.e.d	yes	1
8.d	odd	2	1		2176.1.e.d	yes	1
17.b	even	2	1		2176.1.e.d	yes	1
68.d	odd	2	1		2176.1.e.d	yes	1
136.e	odd	2	1	CM	2176.1.e.a	✓	1
136.h	even	2	1	RM	2176.1.e.a	✓	1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2176.1.e.a	✓	1	1.a	even	1	1	trivial
2176.1.e.a	✓	1	4.b	odd	2	1	CM
2176.1.e.a	✓	1	136.e	odd	2	1	CM
2176.1.e.a	✓	1	136.h	even	2	1	RM
2176.1.e.d	yes	1	8.b	even	2	1
2176.1.e.d	yes	1	8.d	odd	2	1
2176.1.e.d	yes	1	17.b	even	2	1
2176.1.e.d	yes	1	68.d	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{1}^{\mathrm{new}}(2176, [\chi])$:

$ T_{3} $

$ T_{5} + 2 $

$ T_{7} $

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T $ T
$5$	$ T + 2 $ T + 2
$7$	$ T $ T
$11$	$ T $ T
$13$	$ T $ T
$17$	$ T + 1 $ T + 1
$19$	$ T $ T
$23$	$ T $ T
$29$	$ T - 2 $ T - 2
$31$	$ T $ T
$37$	$ T - 2 $ T - 2
$41$	$ T $ T
$43$	$ T $ T
$47$	$ T $ T
$53$	$ T $ T
$59$	$ T $ T
$61$	$ T - 2 $ T - 2
$67$	$ T $ T
$71$	$ T $ T
$73$	$ T $ T
$79$	$ T $ T
$83$	$ T $ T
$89$	$ T - 2 $ T - 2
$97$	$ T $ T
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Level:	\( N \)	\(=\)	\( 2176 = 2^{7} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2176.e (of order \(2\), degree \(1\), minimal)

\(n\)	\(511\)	\(513\)	\(1157\)
\(\chi(n)\)	\(-1\)	\(-1\)	\(-1\)

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