[N,k,chi] = [10,20,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 20, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 20);
N := Newforms(S);
Newform invariants
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
sage: f.q_expansion() # note that sage often uses an isomorphic number field
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.
\( p \) |
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
\( T_{3} - 38628 \)
acting on \(S_{20}^{\mathrm{new}}(\Gamma_0(10))\).
$p$ |
$F_p(T)$ |
$2$ |
\( T + 512 \)
|
$3$ |
\( T - 38628 \)
|
$5$ |
\( T - 1953125 \)
|
$7$ |
\( T + 144185776 \)
|
$11$ |
\( T + 5156500668 \)
|
$13$ |
\( T - 3435515798 \)
|
$17$ |
\( T - 366347849874 \)
|
$19$ |
\( T + 1604379002260 \)
|
$23$ |
\( T + 13649676405552 \)
|
$29$ |
\( T - 50171441088390 \)
|
$31$ |
\( T + 135506765375248 \)
|
$37$ |
\( T - 91268665304894 \)
|
$41$ |
\( T - 827681875418682 \)
|
$43$ |
\( T + 5871395954951812 \)
|
$47$ |
\( T - 13\!\cdots\!64 \)
|
$53$ |
\( T + 36\!\cdots\!62 \)
|
$59$ |
\( T + 12\!\cdots\!20 \)
|
$61$ |
\( T + 71\!\cdots\!98 \)
|
$67$ |
\( T - 31\!\cdots\!44 \)
|
$71$ |
\( T + 24\!\cdots\!08 \)
|
$73$ |
\( T - 37\!\cdots\!58 \)
|
$79$ |
\( T - 16\!\cdots\!80 \)
|
$83$ |
\( T - 18\!\cdots\!48 \)
|
$89$ |
\( T + 30\!\cdots\!90 \)
|
$97$ |
\( T - 69\!\cdots\!34 \)
|
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