[N,k,chi] = [98,18,Mod(1,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.1");
S:= CuspForms(chi, 18);
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
|
\(2\) |
\(-1\) |
\(7\) |
\(-1\) |
This newform does not admit any (nontrivial) inner twists.
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3} + 4626 \)
acting on \(S_{18}^{\mathrm{new}}(\Gamma_0(98))\).
$p$ |
$F_p(T)$ |
$2$ |
\( T - 256 \)
|
$3$ |
\( T + 4626 \)
|
$5$ |
\( T - 851700 \)
|
$7$ |
\( T \)
|
$11$ |
\( T + 586048992 \)
|
$13$ |
\( T - 1042966288 \)
|
$17$ |
\( T - 17187488802 \)
|
$19$ |
\( T - 35251814482 \)
|
$23$ |
\( T - 226463988840 \)
|
$29$ |
\( T + 3381208637406 \)
|
$31$ |
\( T + 257228086436 \)
|
$37$ |
\( T + 40457204426662 \)
|
$41$ |
\( T - 29013168626274 \)
|
$43$ |
\( T - 12667778737448 \)
|
$47$ |
\( T + 286872943920924 \)
|
$53$ |
\( T - 564480420537078 \)
|
$59$ |
\( T + 1802377718625462 \)
|
$61$ |
\( T - 668064962693740 \)
|
$67$ |
\( T - 332890586370548 \)
|
$71$ |
\( T - 4451829225077376 \)
|
$73$ |
\( T - 6135974687950990 \)
|
$79$ |
\( T - 778901092563704 \)
|
$83$ |
\( T - 8884730852317194 \)
|
$89$ |
\( T + 29\!\cdots\!90 \)
|
$97$ |
\( T - 44\!\cdots\!30 \)
|
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