LMFDB - Newform orbit 8664.2.a.h

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [8664,2,Mod(1,8664)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8664, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("8664.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 8664 = 2^{3} \cdot 3 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8664.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,0,1,0,-2,0,-5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$69.1823883112$
Analytic rank:	$2$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 456)
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

1.00000

−2.00000

−5.00000

1.00000

Atkin-Lehner signs

$ p $	Sign
$2$	$ -1 $
$3$	$ -1 $
$19$	$ -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	8664.2.a.h		1
19.b	odd	2	1		8664.2.a.b		1
19.d	odd	6	2		456.2.q.c	✓	2
57.f	even	6	2		1368.2.s.b		2
76.f	even	6	2		912.2.q.c		2
228.n	odd	6	2		2736.2.s.f		2

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
456.2.q.c	✓	2	19.d	odd	6	2
912.2.q.c		2	76.f	even	6	2
1368.2.s.b		2	57.f	even	6	2
2736.2.s.f		2	228.n	odd	6	2
8664.2.a.b		1	19.b	odd	2	1
8664.2.a.h		1	1.a	even	1	1	trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(8664))$:

$ T_{5} + 2 $

T5 + 2

$ T_{7} + 5 $

T7 + 5

$ T_{13} + 5 $

T13 + 5

$ T_{29} + 8 $

T29 + 8

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T - 1 $ T - 1
$5$	$ T + 2 $ T + 2
$7$	$ T + 5 $ T + 5
$11$	$ T + 4 $ T + 4
$13$	$ T + 5 $ T + 5
$17$	$ T $ T
$19$	$ T $ T
$23$	$ T + 6 $ T + 6
$29$	$ T + 8 $ T + 8
$31$	$ T - 1 $ T - 1
$37$	$ T + 7 $ T + 7
$41$	$ T $ T
$43$	$ T + 11 $ T + 11
$47$	$ T - 10 $ T - 10
$53$	$ T + 6 $ T + 6
$59$	$ T + 8 $ T + 8
$61$	$ T + 1 $ T + 1
$67$	$ T + 5 $ T + 5
$71$	$ T + 6 $ T + 6
$73$	$ T - 1 $ T - 1
$79$	$ T - 13 $ T - 13
$83$	$ T + 4 $ T + 4
$89$	$ T - 12 $ T - 12
$97$	$ T + 2 $ T + 2
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Level:	\( N \)	\(=\)	\( 8664 = 2^{3} \cdot 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8664.a (trivial)

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