Properties

Label 5796.2.k.c
Level $5796$
Weight $2$
Character orbit 5796.k
Analytic conductor $46.281$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [5796,2,Mod(5473,5796)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5796, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5796.5473");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5796 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5796.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: \(46.2812930115\)
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
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 80 q^{25} - 48 q^{49} - 40 q^{85}+O(q^{100}) \) Copy content Toggle raw display

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
5473.1 0 0 0 −3.79323 0 −2.36332 1.18943i 0 0 0
5473.2 0 0 0 −3.79323 0 2.36332 1.18943i 0 0 0
5473.3 0 0 0 −3.79323 0 2.36332 + 1.18943i 0 0 0
5473.4 0 0 0 −3.79323 0 −2.36332 + 1.18943i 0 0 0
5473.5 0 0 0 −3.00417 0 1.13593 + 2.38949i 0 0 0
5473.6 0 0 0 −3.00417 0 −1.13593 + 2.38949i 0 0 0
5473.7 0 0 0 −3.00417 0 −1.13593 2.38949i 0 0 0
5473.8 0 0 0 −3.00417 0 1.13593 2.38949i 0 0 0
5473.9 0 0 0 −1.25950 0 0.790195 + 2.52499i 0 0 0
5473.10 0 0 0 −1.25950 0 −0.790195 2.52499i 0 0 0
5473.11 0 0 0 −1.25950 0 −0.790195 + 2.52499i 0 0 0
5473.12 0 0 0 −1.25950 0 0.790195 2.52499i 0 0 0
5473.13 0 0 0 1.25950 0 −0.790195 2.52499i 0 0 0
5473.14 0 0 0 1.25950 0 0.790195 2.52499i 0 0 0
5473.15 0 0 0 1.25950 0 0.790195 + 2.52499i 0 0 0
5473.16 0 0 0 1.25950 0 −0.790195 + 2.52499i 0 0 0
5473.17 0 0 0 3.00417 0 −1.13593 2.38949i 0 0 0
5473.18 0 0 0 3.00417 0 1.13593 2.38949i 0 0 0
5473.19 0 0 0 3.00417 0 1.13593 + 2.38949i 0 0 0
5473.20 0 0 0 3.00417 0 −1.13593 + 2.38949i 0 0 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 5473.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
7.b odd 2 1 inner
21.c even 2 1 inner
23.b odd 2 1 inner
69.c even 2 1 inner
161.c even 2 1 inner
483.c odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 5796.2.k.c 24
3.b odd 2 1 inner 5796.2.k.c 24
7.b odd 2 1 inner 5796.2.k.c 24
21.c even 2 1 inner 5796.2.k.c 24
23.b odd 2 1 inner 5796.2.k.c 24
69.c even 2 1 inner 5796.2.k.c 24
161.c even 2 1 inner 5796.2.k.c 24
483.c odd 2 1 inner 5796.2.k.c 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
5796.2.k.c 24 1.a even 1 1 trivial
5796.2.k.c 24 3.b odd 2 1 inner
5796.2.k.c 24 7.b odd 2 1 inner
5796.2.k.c 24 21.c even 2 1 inner
5796.2.k.c 24 23.b odd 2 1 inner
5796.2.k.c 24 69.c even 2 1 inner
5796.2.k.c 24 161.c even 2 1 inner
5796.2.k.c 24 483.c odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{6} - 25T_{5}^{4} + 167T_{5}^{2} - 206 \) acting on \(S_{2}^{\mathrm{new}}(5796, [\chi])\). Copy content Toggle raw display