![Copy content]()
gp:[N,k,chi] = [320,8,Mod(1,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
![Copy content]()
magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Newform invariants
![Copy content]()
sage:traces = [2,0,-20,0,250,0,-100,0,5554]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == 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 \(\beta = 16\sqrt{19}\).
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
|
| \(2\) |
\( +1 \) |
| \(5\) |
\( -1 \) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{2} + 20T_{3} - 4764 \)
acting on \(S_{8}^{\mathrm{new}}(\Gamma_0(320))\).
![Copy content]()
![Toggle raw display]()
| $p$ |
$F_p(T)$ |
| $2$ |
\( T^{2} \)
![Copy content]()
![Toggle raw display]()
|
| $3$ |
\( T^{2} + 20T - 4764 \)
![Copy content]()
![Toggle raw display]()
|
| $5$ |
\( (T - 125)^{2} \)
![Copy content]()
![Toggle raw display]()
|
| $7$ |
\( T^{2} + 100T - 235836 \)
![Copy content]()
![Toggle raw display]()
|
| $11$ |
\( T^{2} + 4544 T - 6998016 \)
![Copy content]()
![Toggle raw display]()
|
| $13$ |
\( T^{2} + 3540 T - 24961564 \)
![Copy content]()
![Toggle raw display]()
|
| $17$ |
\( T^{2} + 27340 T + 80327844 \)
![Copy content]()
![Toggle raw display]()
|
| $19$ |
\( T^{2} + 38760 T + 367802000 \)
![Copy content]()
![Toggle raw display]()
|
| $23$ |
\( T^{2} + \cdots + 3840033636 \)
![Copy content]()
![Toggle raw display]()
|
| $29$ |
\( T^{2} + \cdots - 27652933500 \)
![Copy content]()
![Toggle raw display]()
|
| $31$ |
\( T^{2} + \cdots + 22939401744 \)
![Copy content]()
![Toggle raw display]()
|
| $37$ |
\( T^{2} + \cdots - 45775154396 \)
![Copy content]()
![Toggle raw display]()
|
| $41$ |
\( T^{2} + \cdots - 227722158876 \)
![Copy content]()
![Toggle raw display]()
|
| $43$ |
\( T^{2} + \cdots - 96985991164 \)
![Copy content]()
![Toggle raw display]()
|
| $47$ |
\( T^{2} + \cdots - 154530884316 \)
![Copy content]()
![Toggle raw display]()
|
| $53$ |
\( T^{2} + \cdots + 1213130224836 \)
![Copy content]()
![Toggle raw display]()
|
| $59$ |
\( T^{2} + \cdots - 3614968086000 \)
![Copy content]()
![Toggle raw display]()
|
| $61$ |
\( T^{2} + \cdots - 672038095516 \)
![Copy content]()
![Toggle raw display]()
|
| $67$ |
\( T^{2} + \cdots + 4620664454244 \)
![Copy content]()
![Toggle raw display]()
|
| $71$ |
\( T^{2} + \cdots - 275746164336 \)
![Copy content]()
![Toggle raw display]()
|
| $73$ |
\( T^{2} + \cdots + 1330152816836 \)
![Copy content]()
![Toggle raw display]()
|
| $79$ |
\( T^{2} + \cdots - 12272229720000 \)
![Copy content]()
![Toggle raw display]()
|
| $83$ |
\( T^{2} + \cdots + 5699002341636 \)
![Copy content]()
![Toggle raw display]()
|
| $89$ |
\( T^{2} + \cdots + 1403196358500 \)
![Copy content]()
![Toggle raw display]()
|
| $97$ |
\( T^{2} + \cdots - 18666217374716 \)
![Copy content]()
![Toggle raw display]()
|
|
show more
|
|
show less
|
