![Copy content]()
gp:[N,k,chi] = [126,8,Mod(1,126)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
![Copy content]()
magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("126.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(126, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
Newform invariants
![Copy content]()
sage:traces = [2,16,0,128,-168]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
![Copy content]()
gp:f = lf[1] \\ Warning: the index may be different
![Copy content]()
sage:f.q_expansion() # note that sage often uses an isomorphic number field
![Copy content]()
gp:mfcoefs(f, 20)
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = 6\sqrt{3691}\).
We also show the integral \(q\)-expansion of the trace form.
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.
![Copy content]()
gp:mfembed(f)
| \( p \) |
Sign
|
| \(2\) |
\( -1 \) |
| \(3\) |
\( +1 \) |
| \(7\) |
\( -1 \) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{2} + 168T_{5} - 125820 \)
acting on \(S_{8}^{\mathrm{new}}(\Gamma_0(126))\).
![Copy content]()
![Toggle raw display]()
| $p$ |
$F_p(T)$ |
| $2$ |
\( (T - 8)^{2} \)
![Copy content]()
![Toggle raw display]()
|
| $3$ |
\( T^{2} \)
![Copy content]()
![Toggle raw display]()
|
| $5$ |
\( T^{2} + 168T - 125820 \)
![Copy content]()
![Toggle raw display]()
|
| $7$ |
\( (T - 343)^{2} \)
![Copy content]()
![Toggle raw display]()
|
| $11$ |
\( T^{2} - 5496 T + 1040580 \)
![Copy content]()
![Toggle raw display]()
|
| $13$ |
\( T^{2} + 5516 T - 68930012 \)
![Copy content]()
![Toggle raw display]()
|
| $17$ |
\( T^{2} - 10248 T + 22933476 \)
![Copy content]()
![Toggle raw display]()
|
| $19$ |
\( T^{2} - 6664 T - 65434352 \)
![Copy content]()
![Toggle raw display]()
|
| $23$ |
\( T^{2} - 45768 T - 264144348 \)
![Copy content]()
![Toggle raw display]()
|
| $29$ |
\( T^{2} + \cdots - 11521995264 \)
![Copy content]()
![Toggle raw display]()
|
| $31$ |
\( T^{2} + \cdots + 8463494032 \)
![Copy content]()
![Toggle raw display]()
|
| $37$ |
\( T^{2} + \cdots + 36113024740 \)
![Copy content]()
![Toggle raw display]()
|
| $41$ |
\( T^{2} + \cdots + 63600513732 \)
![Copy content]()
![Toggle raw display]()
|
| $43$ |
\( T^{2} + \cdots - 234123533936 \)
![Copy content]()
![Toggle raw display]()
|
| $47$ |
\( T^{2} + \cdots - 83318443632 \)
![Copy content]()
![Toggle raw display]()
|
| $53$ |
\( T^{2} + \cdots + 852922259856 \)
![Copy content]()
![Toggle raw display]()
|
| $59$ |
\( T^{2} + \cdots + 3638171701008 \)
![Copy content]()
![Toggle raw display]()
|
| $61$ |
\( T^{2} + \cdots - 2267844045308 \)
![Copy content]()
![Toggle raw display]()
|
| $67$ |
\( T^{2} + \cdots - 20445282631280 \)
![Copy content]()
![Toggle raw display]()
|
| $71$ |
\( T^{2} + \cdots - 10348078644540 \)
![Copy content]()
![Toggle raw display]()
|
| $73$ |
\( T^{2} + \cdots + 6279868157188 \)
![Copy content]()
![Toggle raw display]()
|
| $79$ |
\( T^{2} + \cdots + 11564786539072 \)
![Copy content]()
![Toggle raw display]()
|
| $83$ |
\( T^{2} + \cdots + 1220376268800 \)
![Copy content]()
![Toggle raw display]()
|
| $89$ |
\( T^{2} + \cdots - 56022646632156 \)
![Copy content]()
![Toggle raw display]()
|
| $97$ |
\( T^{2} + \cdots - 103335380149436 \)
![Copy content]()
![Toggle raw display]()
|
|
show more
|
|
show less
|
