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Properties

Label 4140.2.f.d
Level $4140$
Weight $2$
Character orbit 4140.f
Analytic conductor $33.058$
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] = [4140,2,Mod(829,4140)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4140, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4140.829");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4140.f (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: \(33.0580664368\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 8 q^{19} - 8 q^{25} - 12 q^{31} - 28 q^{49} - 16 q^{55} - 16 q^{61} + 8 q^{79} + 12 q^{85} - 16 q^{91}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
829.1 0 0 0 −2.23083 − 0.152950i 0 − 4.09652i 0 0 0
829.2 0 0 0 −2.23083 + 0.152950i 0 4.09652i 0 0 0
829.3 0 0 0 −2.09906 − 0.770673i 0 − 2.34084i 0 0 0
829.4 0 0 0 −2.09906 + 0.770673i 0 2.34084i 0 0 0
829.5 0 0 0 −1.79970 − 1.32706i 0 0.476731i 0 0 0
829.6 0 0 0 −1.79970 + 1.32706i 0 − 0.476731i 0 0 0
829.7 0 0 0 −1.06710 − 1.96502i 0 3.96013i 0 0 0
829.8 0 0 0 −1.06710 + 1.96502i 0 − 3.96013i 0 0 0
829.9 0 0 0 −0.405664 − 2.19896i 0 − 3.23277i 0 0 0
829.10 0 0 0 −0.405664 + 2.19896i 0 3.23277i 0 0 0
829.11 0 0 0 −0.274117 − 2.21920i 0 − 0.615120i 0 0 0
829.12 0 0 0 −0.274117 + 2.21920i 0 0.615120i 0 0 0
829.13 0 0 0 0.274117 − 2.21920i 0 0.615120i 0 0 0
829.14 0 0 0 0.274117 + 2.21920i 0 − 0.615120i 0 0 0
829.15 0 0 0 0.405664 − 2.19896i 0 3.23277i 0 0 0
829.16 0 0 0 0.405664 + 2.19896i 0 − 3.23277i 0 0 0
829.17 0 0 0 1.06710 − 1.96502i 0 − 3.96013i 0 0 0
829.18 0 0 0 1.06710 + 1.96502i 0 3.96013i 0 0 0
829.19 0 0 0 1.79970 − 1.32706i 0 − 0.476731i 0 0 0
829.20 0 0 0 1.79970 + 1.32706i 0 0.476731i 0 0 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 829.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
5.b even 2 1 inner
15.d odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 4140.2.f.d ✓ 24
3.b odd 2 1 inner 4140.2.f.d ✓ 24
5.b even 2 1 inner 4140.2.f.d ✓ 24
15.d odd 2 1 inner 4140.2.f.d ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4140.2.f.d ✓ 24 1.a even 1 1 trivial
4140.2.f.d ✓ 24 3.b odd 2 1 inner
4140.2.f.d ✓ 24 5.b even 2 1 inner
4140.2.f.d ✓ 24 15.d odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7}^{12} + 49T_{7}^{10} + 867T_{7}^{8} + 6563T_{7}^{6} + 18808T_{7}^{4} + 9648T_{7}^{2} + 1296 \) acting on \(S_{2}^{\mathrm{new}}(4140, [\chi])\). Copy content Toggle raw display