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Properties

Label 5472.2.k.d
Level $5472$
Weight $2$
Character orbit 5472.k
Analytic conductor $43.694$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [5472,2,Mod(2431,5472)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5472, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 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("5472.2431");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5472 = 2^{5} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5472.k (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: \(43.6941399860\)
Analytic rank: \(0\)
Dimension: \(40\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 40 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 40 q + 40 q^{25} - 24 q^{49} + 48 q^{61} + 16 q^{73} - 16 q^{85}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2431.1 0 0 0 −4.07207 0 − 1.30098i 0 0 0
2431.2 0 0 0 −4.07207 0 − 1.30098i 0 0 0
2431.3 0 0 0 −4.07207 0 1.30098i 0 0 0
2431.4 0 0 0 −4.07207 0 1.30098i 0 0 0
2431.5 0 0 0 −2.62229 0 − 3.45599i 0 0 0
2431.6 0 0 0 −2.62229 0 − 3.45599i 0 0 0
2431.7 0 0 0 −2.62229 0 3.45599i 0 0 0
2431.8 0 0 0 −2.62229 0 3.45599i 0 0 0
2431.9 0 0 0 −1.78205 0 − 4.26925i 0 0 0
2431.10 0 0 0 −1.78205 0 − 4.26925i 0 0 0
2431.11 0 0 0 −1.78205 0 4.26925i 0 0 0
2431.12 0 0 0 −1.78205 0 4.26925i 0 0 0
2431.13 0 0 0 −1.32365 0 − 0.339676i 0 0 0
2431.14 0 0 0 −1.32365 0 − 0.339676i 0 0 0
2431.15 0 0 0 −1.32365 0 0.339676i 0 0 0
2431.16 0 0 0 −1.32365 0 0.339676i 0 0 0
2431.17 0 0 0 −1.27046 0 − 2.45392i 0 0 0
2431.18 0 0 0 −1.27046 0 2.45392i 0 0 0
2431.19 0 0 0 −1.27046 0 − 2.45392i 0 0 0
2431.20 0 0 0 −1.27046 0 2.45392i 0 0 0
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 2431.40
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
4.b odd 2 1 inner
12.b even 2 1 inner
19.b odd 2 1 inner
57.d even 2 1 inner
76.d even 2 1 inner
228.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 5472.2.k.d ✓ 40
3.b odd 2 1 inner 5472.2.k.d ✓ 40
4.b odd 2 1 inner 5472.2.k.d ✓ 40
12.b even 2 1 inner 5472.2.k.d ✓ 40
19.b odd 2 1 inner 5472.2.k.d ✓ 40
57.d even 2 1 inner 5472.2.k.d ✓ 40
76.d even 2 1 inner 5472.2.k.d ✓ 40
228.b odd 2 1 inner 5472.2.k.d ✓ 40
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
5472.2.k.d ✓ 40 1.a even 1 1 trivial
5472.2.k.d ✓ 40 3.b odd 2 1 inner
5472.2.k.d ✓ 40 4.b odd 2 1 inner
5472.2.k.d ✓ 40 12.b even 2 1 inner
5472.2.k.d ✓ 40 19.b odd 2 1 inner
5472.2.k.d ✓ 40 57.d even 2 1 inner
5472.2.k.d ✓ 40 76.d even 2 1 inner
5472.2.k.d ✓ 40 228.b 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 \(S_{2}^{\mathrm{new}}(5472, [\chi])\):

\( T_{5}^{10} - 30T_{5}^{8} + 281T_{5}^{6} - 1072T_{5}^{4} + 1752T_{5}^{2} - 1024 \) Copy content Toggle raw display
\( T_{31}^{10} - 140T_{31}^{8} + 5400T_{31}^{6} - 76320T_{31}^{4} + 327680T_{31}^{2} - 131072 \) Copy content Toggle raw display