LMFDB - Newform orbit 1568.4.a.i

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1568,4,Mod(1,1568)] 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("1568.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1568, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 1568 = 2^{5} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1568.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,0,0,0,4,0,0,0,-27,0,0,0,92,0,0,0,104,0,0,0,0,0,0,0,-109] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(25)] == traces)

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

Self dual:	yes
Analytic conductor:	$92.5149948890$
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:	$N(\mathrm{U}(1))$

$q$-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

−27.0000

Atkin-Lehner signs

$ p $	Sign
$2$	$ -1 $
$7$	$ -1 $

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1568.4.a.i	yes	1
4.b	odd	2	1	CM	1568.4.a.i	yes	1
7.b	odd	2	1		1568.4.a.h	✓	1
28.d	even	2	1		1568.4.a.h	✓	1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1568.4.a.h	✓	1	7.b	odd	2	1
1568.4.a.h	✓	1	28.d	even	2	1
1568.4.a.i	yes	1	1.a	even	1	1	trivial
1568.4.a.i	yes	1	4.b	odd	2	1	CM

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(1568))$:

$ T_{3} $

T3

$ T_{5} - 4 $

T5 - 4

$ T_{11} $

T11

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T $ T
$5$	$ T - 4 $ T - 4
$7$	$ T $ T
$11$	$ T $ T
$13$	$ T - 92 $ T - 92
$17$	$ T - 104 $ T - 104
$19$	$ T $ T
$23$	$ T $ T
$29$	$ T - 130 $ T - 130
$31$	$ T $ T
$37$	$ T + 214 $ T + 214
$41$	$ T + 472 $ T + 472
$43$	$ T $ T
$47$	$ T $ T
$53$	$ T - 518 $ T - 518
$59$	$ T $ T
$61$	$ T - 468 $ T - 468
$67$	$ T $ T
$71$	$ T $ T
$73$	$ T + 592 $ T + 592
$79$	$ T $ T
$83$	$ T $ T
$89$	$ T - 176 $ T - 176
$97$	$ T - 1816 $ T - 1816
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Level:	\( N \)	\(=\)	\( 1568 = 2^{5} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1568.a (trivial)

\(n\):		e.g. 2-40 or 80-90
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