Properties

Label 639.3.d.d
Level $639$
Weight $3$
Character orbit 639.d
Analytic conductor $17.411$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [639,3,Mod(496,639)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(639, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("639.496");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 639 = 3^{2} \cdot 71 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 639.d (of order \(2\), degree \(1\), 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: no
Analytic conductor: \(17.4114888926\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 60 q^{4}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 60 q^{4} + 44 q^{10} + 156 q^{16} - 32 q^{19} + 60 q^{25} + 28 q^{37} + 108 q^{40} + 76 q^{43} - 56 q^{49} + 112 q^{58} + 264 q^{64} + 128 q^{73} - 404 q^{76} - 308 q^{79} - 900 q^{91}+O(q^{100}) \) Copy content Toggle raw display

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
496.1 −3.83989 0 10.7448 −2.25297 0 11.1817i −25.8992 0 8.65118
496.2 −3.83989 0 10.7448 −2.25297 0 11.1817i −25.8992 0 8.65118
496.3 −3.14297 0 5.87828 6.38552 0 5.89299i −5.90338 0 −20.0695
496.4 −3.14297 0 5.87828 6.38552 0 5.89299i −5.90338 0 −20.0695
496.5 −2.96982 0 4.81983 −6.96665 0 1.70133i −2.43476 0 20.6897
496.6 −2.96982 0 4.81983 −6.96665 0 1.70133i −2.43476 0 20.6897
496.7 −2.02401 0 0.0966251 −0.798722 0 4.78394i 7.90048 0 1.61662
496.8 −2.02401 0 0.0966251 −0.798722 0 4.78394i 7.90048 0 1.61662
496.9 −1.07799 0 −2.83793 3.69839 0 9.66006i 7.37125 0 −3.98684
496.10 −1.07799 0 −2.83793 3.69839 0 9.66006i 7.37125 0 −3.98684
496.11 −0.546276 0 −3.70158 −7.50327 0 5.39869i 4.20719 0 4.09886
496.12 −0.546276 0 −3.70158 −7.50327 0 5.39869i 4.20719 0 4.09886
496.13 0.546276 0 −3.70158 7.50327 0 5.39869i −4.20719 0 4.09886
496.14 0.546276 0 −3.70158 7.50327 0 5.39869i −4.20719 0 4.09886
496.15 1.07799 0 −2.83793 −3.69839 0 9.66006i −7.37125 0 −3.98684
496.16 1.07799 0 −2.83793 −3.69839 0 9.66006i −7.37125 0 −3.98684
496.17 2.02401 0 0.0966251 0.798722 0 4.78394i −7.90048 0 1.61662
496.18 2.02401 0 0.0966251 0.798722 0 4.78394i −7.90048 0 1.61662
496.19 2.96982 0 4.81983 6.96665 0 1.70133i 2.43476 0 20.6897
496.20 2.96982 0 4.81983 6.96665 0 1.70133i 2.43476 0 20.6897
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 496.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
71.b odd 2 1 inner
213.b even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 639.3.d.d 24
3.b odd 2 1 inner 639.3.d.d 24
71.b odd 2 1 inner 639.3.d.d 24
213.b even 2 1 inner 639.3.d.d 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
639.3.d.d 24 1.a even 1 1 trivial
639.3.d.d 24 3.b odd 2 1 inner
639.3.d.d 24 71.b odd 2 1 inner
639.3.d.d 24 213.b even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{12} - 39T_{2}^{10} + 555T_{2}^{8} - 3514T_{2}^{6} + 9483T_{2}^{4} - 8647T_{2}^{2} + 1825 \) acting on \(S_{3}^{\mathrm{new}}(639, [\chi])\). Copy content Toggle raw display