![Copy content]()
gp:[N,k,chi] = [80,10,Mod(1,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 10, names="a")
![Copy content]()
magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("80.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Newform invariants
![Copy content]()
sage:traces = [2,0,-108]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == 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 \(\beta = 24\sqrt{46}\).
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
\( T_{3}^{2} + 108T_{3} - 23580 \)
acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(80))\).
![Copy content]()
![Toggle raw display]()
| $p$ |
$F_p(T)$ |
| $2$ |
\( T^{2} \)
![Copy content]()
![Toggle raw display]()
|
| $3$ |
\( T^{2} + 108T - 23580 \)
![Copy content]()
![Toggle raw display]()
|
| $5$ |
\( (T + 625)^{2} \)
![Copy content]()
![Toggle raw display]()
|
| $7$ |
\( T^{2} - 908 T - 4271708 \)
![Copy content]()
![Toggle raw display]()
|
| $11$ |
\( T^{2} + 25120 T - 318008576 \)
![Copy content]()
![Toggle raw display]()
|
| $13$ |
\( T^{2} + \cdots - 2558426108 \)
![Copy content]()
![Toggle raw display]()
|
| $17$ |
\( T^{2} + \cdots + 7111617700 \)
![Copy content]()
![Toggle raw display]()
|
| $19$ |
\( T^{2} + \cdots - 273876705776 \)
![Copy content]()
![Toggle raw display]()
|
| $23$ |
\( T^{2} + \cdots + 363587809732 \)
![Copy content]()
![Toggle raw display]()
|
| $29$ |
\( T^{2} + \cdots + 480965491876 \)
![Copy content]()
![Toggle raw display]()
|
| $31$ |
\( T^{2} + \cdots + 20138081829520 \)
![Copy content]()
![Toggle raw display]()
|
| $37$ |
\( T^{2} + \cdots - 155824381229436 \)
![Copy content]()
![Toggle raw display]()
|
| $41$ |
\( T^{2} + \cdots - 149515623312732 \)
![Copy content]()
![Toggle raw display]()
|
| $43$ |
\( T^{2} + \cdots + 69358444830148 \)
![Copy content]()
![Toggle raw display]()
|
| $47$ |
\( T^{2} + \cdots - 11\!\cdots\!84 \)
![Copy content]()
![Toggle raw display]()
|
| $53$ |
\( T^{2} + \cdots - 31\!\cdots\!84 \)
![Copy content]()
![Toggle raw display]()
|
| $59$ |
\( T^{2} + \cdots - 58\!\cdots\!52 \)
![Copy content]()
![Toggle raw display]()
|
| $61$ |
\( T^{2} + \cdots - 10\!\cdots\!60 \)
![Copy content]()
![Toggle raw display]()
|
| $67$ |
\( T^{2} + \cdots - 32\!\cdots\!48 \)
![Copy content]()
![Toggle raw display]()
|
| $71$ |
\( T^{2} + \cdots - 23\!\cdots\!40 \)
![Copy content]()
![Toggle raw display]()
|
| $73$ |
\( T^{2} + \cdots + 12\!\cdots\!12 \)
![Copy content]()
![Toggle raw display]()
|
| $79$ |
\( T^{2} + \cdots + 36\!\cdots\!80 \)
![Copy content]()
![Toggle raw display]()
|
| $83$ |
\( T^{2} + \cdots - 33\!\cdots\!32 \)
![Copy content]()
![Toggle raw display]()
|
| $89$ |
\( T^{2} + \cdots - 11\!\cdots\!36 \)
![Copy content]()
![Toggle raw display]()
|
| $97$ |
\( T^{2} + \cdots + 98\!\cdots\!96 \)
![Copy content]()
![Toggle raw display]()
|
|
show more
|
|
show less
|
