[N,k,chi] = [48,24,Mod(1,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 24, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.1");
S:= CuspForms(chi, 24);
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
|
\(2\) |
\(-1\) |
\(3\) |
\(-1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5} + 9019770 \)
acting on \(S_{24}^{\mathrm{new}}(\Gamma_0(48))\).
$p$ |
$F_p(T)$ |
$2$ |
\( T \)
|
$3$ |
\( T - 177147 \)
|
$5$ |
\( T + 9019770 \)
|
$7$ |
\( T + 515282432 \)
|
$11$ |
\( T - 855114401460 \)
|
$13$ |
\( T + 8296664277034 \)
|
$17$ |
\( T + 4352120377758 \)
|
$19$ |
\( T - 458349498184876 \)
|
$23$ |
\( T - 6002199220659000 \)
|
$29$ |
\( T + 53\!\cdots\!94 \)
|
$31$ |
\( T + 76\!\cdots\!68 \)
|
$37$ |
\( T - 10\!\cdots\!34 \)
|
$41$ |
\( T - 27\!\cdots\!34 \)
|
$43$ |
\( T + 63\!\cdots\!88 \)
|
$47$ |
\( T - 16\!\cdots\!60 \)
|
$53$ |
\( T - 13\!\cdots\!22 \)
|
$59$ |
\( T + 28\!\cdots\!60 \)
|
$61$ |
\( T - 26\!\cdots\!10 \)
|
$67$ |
\( T - 17\!\cdots\!88 \)
|
$71$ |
\( T - 17\!\cdots\!80 \)
|
$73$ |
\( T + 37\!\cdots\!54 \)
|
$79$ |
\( T - 85\!\cdots\!48 \)
|
$83$ |
\( T + 11\!\cdots\!96 \)
|
$89$ |
\( T - 32\!\cdots\!22 \)
|
$97$ |
\( T + 43\!\cdots\!06 \)
|
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