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Properties

Label 5148.2.e.f
Level $5148$
Weight $2$
Character orbit 5148.e
Analytic conductor $41.107$
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] = [5148,2,Mod(1585,5148)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5148, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5148.1585");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5148 = 2^{2} \cdot 3^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5148.e (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: \(41.1069869606\)
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
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 4 q^{13} - 40 q^{25} - 32 q^{43} - 40 q^{49} + 48 q^{61} - 8 q^{79} + 48 q^{91}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1585.1 0 0 0 − 4.09104i 0 − 2.82225i 0 0 0
1585.2 0 0 0 − 4.09104i 0 2.82225i 0 0 0
1585.3 0 0 0 − 3.48845i 0 − 4.71713i 0 0 0
1585.4 0 0 0 − 3.48845i 0 4.71713i 0 0 0
1585.5 0 0 0 − 2.37345i 0 − 2.26320i 0 0 0
1585.6 0 0 0 − 2.37345i 0 2.26320i 0 0 0
1585.7 0 0 0 − 1.73454i 0 − 1.06182i 0 0 0
1585.8 0 0 0 − 1.73454i 0 1.06182i 0 0 0
1585.9 0 0 0 − 1.12532i 0 − 3.92741i 0 0 0
1585.10 0 0 0 − 1.12532i 0 3.92741i 0 0 0
1585.11 0 0 0 − 1.08900i 0 − 0.330839i 0 0 0
1585.12 0 0 0 − 1.08900i 0 0.330839i 0 0 0
1585.13 0 0 0 1.08900i 0 − 0.330839i 0 0 0
1585.14 0 0 0 1.08900i 0 0.330839i 0 0 0
1585.15 0 0 0 1.12532i 0 − 3.92741i 0 0 0
1585.16 0 0 0 1.12532i 0 3.92741i 0 0 0
1585.17 0 0 0 1.73454i 0 − 1.06182i 0 0 0
1585.18 0 0 0 1.73454i 0 1.06182i 0 0 0
1585.19 0 0 0 2.37345i 0 − 2.26320i 0 0 0
1585.20 0 0 0 2.37345i 0 2.26320i 0 0 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1585.24
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 5148.2.e.f ✓ 24
3.b odd 2 1 inner 5148.2.e.f ✓ 24
13.b even 2 1 inner 5148.2.e.f ✓ 24
39.d odd 2 1 inner 5148.2.e.f ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
5148.2.e.f ✓ 24 1.a even 1 1 trivial
5148.2.e.f ✓ 24 3.b odd 2 1 inner
5148.2.e.f ✓ 24 13.b even 2 1 inner
5148.2.e.f ✓ 24 39.d odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(5148, [\chi])\):

\( T_{5}^{12} + 40T_{5}^{10} + 564T_{5}^{8} + 3460T_{5}^{6} + 9676T_{5}^{4} + 11844T_{5}^{2} + 5184 \) Copy content Toggle raw display
\( T_{7}^{12} + 52T_{7}^{10} + 940T_{7}^{8} + 7120T_{7}^{6} + 21568T_{7}^{4} + 18064T_{7}^{2} + 1728 \) Copy content Toggle raw display