[N,k,chi] = [6,22,Mod(1,6)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6.1");
S:= CuspForms(chi, 22);
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
\( T_{5} - 12954174 \)
acting on \(S_{22}^{\mathrm{new}}(\Gamma_0(6))\).
$p$ |
$F_p(T)$ |
$2$ |
\( T - 1024 \)
|
$3$ |
\( T + 59049 \)
|
$5$ |
\( T - 12954174 \)
|
$7$ |
\( T + 479513104 \)
|
$11$ |
\( T - 115657781700 \)
|
$13$ |
\( T - 295658246702 \)
|
$17$ |
\( T - 6626983431906 \)
|
$19$ |
\( T - 28576184164796 \)
|
$23$ |
\( T - 335385196791000 \)
|
$29$ |
\( T + 699224214482106 \)
|
$31$ |
\( T + 3484957262657992 \)
|
$37$ |
\( T + 35\!\cdots\!98 \)
|
$41$ |
\( T - 6132056240639994 \)
|
$43$ |
\( T - 23\!\cdots\!96 \)
|
$47$ |
\( T + 58\!\cdots\!00 \)
|
$53$ |
\( T + 13\!\cdots\!06 \)
|
$59$ |
\( T - 23\!\cdots\!00 \)
|
$61$ |
\( T - 99\!\cdots\!90 \)
|
$67$ |
\( T - 26\!\cdots\!96 \)
|
$71$ |
\( T + 13\!\cdots\!00 \)
|
$73$ |
\( T - 90\!\cdots\!02 \)
|
$79$ |
\( T + 77\!\cdots\!92 \)
|
$83$ |
\( T + 15\!\cdots\!88 \)
|
$89$ |
\( T - 25\!\cdots\!18 \)
|
$97$ |
\( T + 10\!\cdots\!98 \)
|
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