[N,k,chi] = [141,4,Mod(1,141)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(141, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("141.1");
S:= CuspForms(chi, 4);
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
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \sqrt{111}\).
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.
\( p \) |
Sign
|
\(3\) |
\(-1\) |
\(47\) |
\(-1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2} - 4 \)
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(141))\).
$p$ |
$F_p(T)$ |
$2$ |
\( (T - 4)^{2} \)
|
$3$ |
\( (T - 3)^{2} \)
|
$5$ |
\( T^{2} - 6T - 102 \)
|
$7$ |
\( T^{2} - 20T - 344 \)
|
$11$ |
\( T^{2} - 84T + 1320 \)
|
$13$ |
\( T^{2} - 12T - 1740 \)
|
$17$ |
\( T^{2} + 60T - 6204 \)
|
$19$ |
\( T^{2} + 38T + 250 \)
|
$23$ |
\( T^{2} + 236T + 9928 \)
|
$29$ |
\( T^{2} - 98T - 3038 \)
|
$31$ |
\( T^{2} + 198T - 39150 \)
|
$37$ |
\( T^{2} + 84T - 19992 \)
|
$41$ |
\( T^{2} - 166T - 129086 \)
|
$43$ |
\( T^{2} - 102T - 37470 \)
|
$47$ |
\( (T - 47)^{2} \)
|
$53$ |
\( T^{2} + 856T + 161428 \)
|
$59$ |
\( T^{2} - 552T - 179568 \)
|
$61$ |
\( T^{2} + 68T - 52568 \)
|
$67$ |
\( T^{2} + 430T + 46114 \)
|
$71$ |
\( T^{2} - 1404 T + 428868 \)
|
$73$ |
\( T^{2} + 752T - 18908 \)
|
$79$ |
\( T^{2} - 388T - 389048 \)
|
$83$ |
\( T^{2} - 100T - 638636 \)
|
$89$ |
\( T^{2} - 944T - 843260 \)
|
$97$ |
\( T^{2} + 1548 T + 438792 \)
|
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