[N,k,chi] = [2,32,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 32, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 32);
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
|
\(2\) |
\(-1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3} + 19984212 \)
acting on \(S_{32}^{\mathrm{new}}(\Gamma_0(2))\).
$p$ |
$F_p(T)$ |
$2$ |
\( T - 32768 \)
|
$3$ |
\( T + 19984212 \)
|
$5$ |
\( T - 42951708750 \)
|
$7$ |
\( T + 16835358997576 \)
|
$11$ |
\( T + 7207832704992348 \)
|
$13$ |
\( T + 27\!\cdots\!82 \)
|
$17$ |
\( T + 16\!\cdots\!06 \)
|
$19$ |
\( T - 10\!\cdots\!40 \)
|
$23$ |
\( T + 30\!\cdots\!72 \)
|
$29$ |
\( T - 34\!\cdots\!90 \)
|
$31$ |
\( T - 16\!\cdots\!12 \)
|
$37$ |
\( T + 25\!\cdots\!46 \)
|
$41$ |
\( T + 92\!\cdots\!38 \)
|
$43$ |
\( T - 58\!\cdots\!88 \)
|
$47$ |
\( T + 91\!\cdots\!56 \)
|
$53$ |
\( T - 58\!\cdots\!98 \)
|
$59$ |
\( T + 32\!\cdots\!20 \)
|
$61$ |
\( T - 40\!\cdots\!22 \)
|
$67$ |
\( T - 16\!\cdots\!64 \)
|
$71$ |
\( T + 68\!\cdots\!68 \)
|
$73$ |
\( T + 23\!\cdots\!62 \)
|
$79$ |
\( T + 63\!\cdots\!20 \)
|
$83$ |
\( T + 28\!\cdots\!12 \)
|
$89$ |
\( T - 19\!\cdots\!10 \)
|
$97$ |
\( T + 77\!\cdots\!86 \)
|
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