LMFDB - Newform orbit 32.7.d.a

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [32,7,Mod(15,32)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(32, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("32.15");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 32 = 2^{5} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	32.d (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:	$7.36173067584$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 8)
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 $\left(\mathbb{Z}/32\mathbb{Z}\right)^\times$.

$n$	$5$	$31$
$\chi(n)$	$1$	$1$

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} $

15.1

−46.0000

1387.00

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	32.7.d.a		1
3.b	odd	2	1		288.7.b.a		1
4.b	odd	2	1		8.7.d.a	✓	1
8.b	even	2	1		8.7.d.a	✓	1
8.d	odd	2	1	CM	32.7.d.a		1
12.b	even	2	1		72.7.b.a		1
16.e	even	4	2		256.7.c.d		2
16.f	odd	4	2		256.7.c.d		2
24.f	even	2	1		288.7.b.a		1
24.h	odd	2	1		72.7.b.a		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
8.7.d.a	✓	1	4.b	odd	2	1
8.7.d.a	✓	1	8.b	even	2	1
32.7.d.a		1	1.a	even	1	1	trivial
32.7.d.a		1	8.d	odd	2	1	CM
72.7.b.a		1	12.b	even	2	1
72.7.b.a		1	24.h	odd	2	1
256.7.c.d		2	16.e	even	4	2
256.7.c.d		2	16.f	odd	4	2
288.7.b.a		1	3.b	odd	2	1
288.7.b.a		1	24.f	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{3} + 46 $ T3 + 46 acting on $S_{7}^{\mathrm{new}}(32, [\chi])$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T + 46 $ T + 46
$5$	$ T $ T
$7$	$ T $ T
$11$	$ T - 2338 $ T - 2338
$13$	$ T $ T
$17$	$ T + 1726 $ T + 1726
$19$	$ T - 2482 $ T - 2482
$23$	$ T $ T
$29$	$ T $ T
$31$	$ T $ T
$37$	$ T $ T
$41$	$ T - 134642 $ T - 134642
$43$	$ T - 74914 $ T - 74914
$47$	$ T $ T
$53$	$ T $ T
$59$	$ T + 304958 $ T + 304958
$61$	$ T $ T
$67$	$ T - 596626 $ T - 596626
$71$	$ T $ T
$73$	$ T + 593134 $ T + 593134
$79$	$ T $ T
$83$	$ T + 678926 $ T + 678926
$89$	$ T + 357262 $ T + 357262
$97$	$ T - 1822754 $ T - 1822754
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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:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	32.d (of order \(2\), degree \(1\), not minimal)

\(n\)	\(5\)	\(31\)
\(\chi(n)\)	\(1\)	\(1\)

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