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Properties

Label 1584.2.cd.e
Level $1584$
Weight $2$
Character orbit 1584.cd
Analytic conductor $12.648$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1584,2,Mod(17,1584)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1584, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 5, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1584.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1584.cd (of order \(10\), degree \(4\), not 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: \(12.6483036802\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{10})\)
Twist minimal: no (minimal twist has level 792)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 12 q^{11} - 16 q^{17} + 6 q^{25} + 2 q^{29} - 2 q^{31} + 14 q^{35} - 12 q^{37} + 24 q^{41} - 20 q^{47} + 14 q^{49} - 50 q^{53} - 4 q^{55} - 20 q^{59} + 20 q^{61} + 16 q^{65} - 8 q^{67} + 20 q^{71} + 50 q^{73} + 40 q^{77} - 20 q^{79} + 44 q^{83} + 60 q^{85} - 40 q^{95} - 16 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
17.1 0 0 0 −2.16251 − 0.702643i 0 −1.01751 − 1.40048i 0 0 0
17.2 0 0 0 −1.81256 − 0.588938i 0 −1.07016 − 1.47295i 0 0 0
17.3 0 0 0 −0.577828 − 0.187748i 0 1.32737 + 1.82696i 0 0 0
17.4 0 0 0 0.328347 + 0.106686i 0 2.14419 + 2.95122i 0 0 0
17.5 0 0 0 2.60225 + 0.845523i 0 −0.787246 − 1.08355i 0 0 0
17.6 0 0 0 3.85837 + 1.25366i 0 1.63943 + 2.25649i 0 0 0
161.1 0 0 0 −2.16697 − 2.98258i 0 −1.15726 + 0.376015i 0 0 0
161.2 0 0 0 −1.79418 − 2.46948i 0 −1.84318 + 0.598887i 0 0 0
161.3 0 0 0 −0.135726 − 0.186811i 0 3.35488 − 1.09007i 0 0 0
161.4 0 0 0 −0.0934478 − 0.128620i 0 −0.248702 + 0.0808083i 0 0 0
161.5 0 0 0 0.769593 + 1.05925i 0 2.31885 − 0.753440i 0 0 0
161.6 0 0 0 1.18466 + 1.63055i 0 −4.66066 + 1.51434i 0 0 0
305.1 0 0 0 −2.16697 + 2.98258i 0 −1.15726 − 0.376015i 0 0 0
305.2 0 0 0 −1.79418 + 2.46948i 0 −1.84318 − 0.598887i 0 0 0
305.3 0 0 0 −0.135726 + 0.186811i 0 3.35488 + 1.09007i 0 0 0
305.4 0 0 0 −0.0934478 + 0.128620i 0 −0.248702 − 0.0808083i 0 0 0
305.5 0 0 0 0.769593 − 1.05925i 0 2.31885 + 0.753440i 0 0 0
305.6 0 0 0 1.18466 − 1.63055i 0 −4.66066 − 1.51434i 0 0 0
1025.1 0 0 0 −2.16251 + 0.702643i 0 −1.01751 + 1.40048i 0 0 0
1025.2 0 0 0 −1.81256 + 0.588938i 0 −1.07016 + 1.47295i 0 0 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 17.6
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
33.f even 10 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1584.2.cd.e 24
3.b odd 2 1 1584.2.cd.f 24
4.b odd 2 1 792.2.bv.b yes 24
11.d odd 10 1 1584.2.cd.f 24
12.b even 2 1 792.2.bv.a ✓ 24
33.f even 10 1 inner 1584.2.cd.e 24
44.g even 10 1 792.2.bv.a ✓ 24
132.n odd 10 1 792.2.bv.b yes 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
792.2.bv.a ✓ 24 12.b even 2 1
792.2.bv.a ✓ 24 44.g even 10 1
792.2.bv.b yes 24 4.b odd 2 1
792.2.bv.b yes 24 132.n odd 10 1
1584.2.cd.e 24 1.a even 1 1 trivial
1584.2.cd.e 24 33.f even 10 1 inner
1584.2.cd.f 24 3.b odd 2 1
1584.2.cd.f 24 11.d odd 10 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{24} - 18 T_{5}^{22} - 70 T_{5}^{21} + 223 T_{5}^{20} + 1260 T_{5}^{19} - 13 T_{5}^{18} + \cdots + 121 \) acting on \(S_{2}^{\mathrm{new}}(1584, [\chi])\). Copy content Toggle raw display