LMFDB - Newform orbit 1007.1.d.b

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1007,1,Mod(1006,1007)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1007.1006"); S:= CuspForms(chi, 1); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1007, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

Level:	$ N $	$=$	$ 1007 = 19 \cdot 53 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1007.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [1,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$0.502558467721$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.1007.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.0.19266931.1
Stark unit:	Root of $x^{6} - 20390x^{5} + 4192063x^{4} - 407408756x^{3} + 4192063x^{2} - 20390x + 1$

$q$-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 $\left(\mathbb{Z}/1007\mathbb{Z}\right)^\times$.

$n$	$267$	$743$
$\chi(n)$	$-1$	$-1$

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} $

1006.1

1.00000

2.00000

−1.00000

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
1007.d	odd	2	1	CM by $\Q(\sqrt{-1007}) $

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1007.1.d.b	yes	1
19.b	odd	2	1		1007.1.d.a	✓	1
53.b	even	2	1		1007.1.d.a	✓	1
1007.d	odd	2	1	CM	1007.1.d.b	yes	1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1007.1.d.a	✓	1	19.b	odd	2	1
1007.1.d.a	✓	1	53.b	even	2	1
1007.1.d.b	yes	1	1.a	even	1	1	trivial
1007.1.d.b	yes	1	1007.d	odd	2	1	CM

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{2} - 1 $ T2 - 1 acting on $S_{1}^{\mathrm{new}}(1007, [\chi])$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T - 1 $ T - 1
$3$	$ T - 1 $ T - 1
$5$	$ T $ T
$7$	$ T - 2 $ T - 2
$11$	$ T + 1 $ T + 1
$13$	$ T $ T
$17$	$ T + 1 $ T + 1
$19$	$ T + 1 $ T + 1
$23$	$ T $ T
$29$	$ T $ T
$31$	$ T - 1 $ T - 1
$37$	$ T $ T
$41$	$ T + 2 $ T + 2
$43$	$ T + 1 $ T + 1
$47$	$ T - 2 $ T - 2
$53$	$ T + 1 $ T + 1
$59$	$ T $ T
$61$	$ T $ T
$67$	$ T - 1 $ T - 1
$71$	$ T - 1 $ T - 1
$73$	$ T $ T
$79$	$ T + 2 $ T + 2
$83$	$ T $ T
$89$	$ T $ T
$97$	$ T $ T
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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1007 = 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1007.d (of order \(2\), degree \(1\), minimal)

\(n\)	\(267\)	\(743\)
\(\chi(n)\)	\(-1\)	\(-1\)

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