LMFDB - Newform orbit 828.4.a.b

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [828,4,Mod(1,828)] 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("828.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(828, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 828 = 2^{2} \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	828.a (trivial)

Newform invariants

comment:select newform

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

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

Self dual:	yes
Analytic conductor:	$48.8535814848$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 276)
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

−2.00000

−22.0000

Atkin-Lehner signs

$ p $	Sign
$2$	$ -1 $
$3$	$ -1 $
$23$	$ +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	828.4.a.b		1
3.b	odd	2	1		276.4.a.a	✓	1
12.b	even	2	1		1104.4.a.b		1

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
276.4.a.a	✓	1	3.b	odd	2	1
828.4.a.b		1	1.a	even	1	1	trivial
1104.4.a.b		1	12.b	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{5} + 2 $ T5 + 2 acting on $S_{4}^{\mathrm{new}}(\Gamma_0(828))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$ T $ T
$3$	$ T $ T
$5$	$ T + 2 $ T + 2
$7$	$ T + 22 $ T + 22
$11$	$ T - 14 $ T - 14
$13$	$ T + 50 $ T + 50
$17$	$ T - 52 $ T - 52
$19$	$ T + 20 $ T + 20
$23$	$ T + 23 $ T + 23
$29$	$ T - 74 $ T - 74
$31$	$ T - 24 $ T - 24
$37$	$ T - 104 $ T - 104
$41$	$ T - 30 $ T - 30
$43$	$ T - 112 $ T - 112
$47$	$ T - 288 $ T - 288
$53$	$ T - 386 $ T - 386
$59$	$ T - 204 $ T - 204
$61$	$ T + 308 $ T + 308
$67$	$ T - 152 $ T - 152
$71$	$ T - 720 $ T - 720
$73$	$ T - 486 $ T - 486
$79$	$ T - 462 $ T - 462
$83$	$ T + 742 $ T + 742
$89$	$ T + 180 $ T + 180
$97$	$ T - 786 $ T - 786
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Elliptic curves over $\Q$
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Level:	\( N \)	\(=\)	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	828.a (trivial)

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