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Properties

Label 7920.2.k.d
Level $7920$
Weight $2$
Character orbit 7920.k
Analytic conductor $63.242$
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] = [7920,2,Mod(1871,7920)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7920, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("7920.1871");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7920 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7920.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: \(63.2415184009\)
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
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 24 q^{11} + 16 q^{13} + 32 q^{23} - 24 q^{25} - 32 q^{37} - 32 q^{47} - 24 q^{49} - 32 q^{59} - 16 q^{61} + 32 q^{73} - 16 q^{83} + 16 q^{95}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1871.1 0 0 0 − 1.00000i 0 − 5.02407i 0 0 0
1871.2 0 0 0 − 1.00000i 0 − 3.43776i 0 0 0
1871.3 0 0 0 − 1.00000i 0 − 3.14486i 0 0 0
1871.4 0 0 0 − 1.00000i 0 − 2.14586i 0 0 0
1871.5 0 0 0 − 1.00000i 0 − 1.30904i 0 0 0
1871.6 0 0 0 − 1.00000i 0 0.340627i 0 0 0
1871.7 0 0 0 − 1.00000i 0 0.819735i 0 0 0
1871.8 0 0 0 − 1.00000i 0 1.96396i 0 0 0
1871.9 0 0 0 − 1.00000i 0 2.41962i 0 0 0
1871.10 0 0 0 − 1.00000i 0 2.50908i 0 0 0
1871.11 0 0 0 − 1.00000i 0 2.67451i 0 0 0
1871.12 0 0 0 − 1.00000i 0 4.33405i 0 0 0
1871.13 0 0 0 1.00000i 0 − 4.33405i 0 0 0
1871.14 0 0 0 1.00000i 0 − 2.67451i 0 0 0
1871.15 0 0 0 1.00000i 0 − 2.50908i 0 0 0
1871.16 0 0 0 1.00000i 0 − 2.41962i 0 0 0
1871.17 0 0 0 1.00000i 0 − 1.96396i 0 0 0
1871.18 0 0 0 1.00000i 0 − 0.819735i 0 0 0
1871.19 0 0 0 1.00000i 0 − 0.340627i 0 0 0
1871.20 0 0 0 1.00000i 0 1.30904i 0 0 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1871.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
12.b even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 7920.2.k.d yes 24
3.b odd 2 1 7920.2.k.c ✓ 24
4.b odd 2 1 7920.2.k.c ✓ 24
12.b even 2 1 inner 7920.2.k.d yes 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
7920.2.k.c ✓ 24 3.b odd 2 1
7920.2.k.c ✓ 24 4.b odd 2 1
7920.2.k.d yes 24 1.a even 1 1 trivial
7920.2.k.d yes 24 12.b even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(7920, [\chi])\):

\( T_{7}^{24} + 96 T_{7}^{22} + 3912 T_{7}^{20} + 89408 T_{7}^{18} + 1274328 T_{7}^{16} + 11887488 T_{7}^{14} + \cdots + 34668544 \) Copy content Toggle raw display
\( T_{23}^{12} - 16 T_{23}^{11} + 20 T_{23}^{10} + 928 T_{23}^{9} - 5436 T_{23}^{8} - 896 T_{23}^{7} + \cdots + 102400 \) Copy content Toggle raw display