[N,k,chi] = [72,16,Mod(1,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 16, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.1");
S:= CuspForms(chi, 16);
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
\( T_{5} - 42010 \)
acting on \(S_{16}^{\mathrm{new}}(\Gamma_0(72))\).
$p$ |
$F_p(T)$ |
$2$ |
\( T \)
|
$3$ |
\( T \)
|
$5$ |
\( T - 42010 \)
|
$7$ |
\( T - 385728 \)
|
$11$ |
\( T + 20444300 \)
|
$13$ |
\( T - 75221302 \)
|
$17$ |
\( T + 639707746 \)
|
$19$ |
\( T - 267006356 \)
|
$23$ |
\( T + 571925576 \)
|
$29$ |
\( T - 62437913154 \)
|
$31$ |
\( T + 1243357000 \)
|
$37$ |
\( T + 408247831602 \)
|
$41$ |
\( T - 1376815491990 \)
|
$43$ |
\( T + 1923521494772 \)
|
$47$ |
\( T - 4743411679104 \)
|
$53$ |
\( T - 3260491936570 \)
|
$59$ |
\( T + 6734040423500 \)
|
$61$ |
\( T + 10498750519274 \)
|
$67$ |
\( T - 42186307399892 \)
|
$71$ |
\( T + 81526680652600 \)
|
$73$ |
\( T + 37550447155142 \)
|
$79$ |
\( T - 169301409686344 \)
|
$83$ |
\( T + 357833604131476 \)
|
$89$ |
\( T - 157672146871542 \)
|
$97$ |
\( T + 1220442820436926 \)
|
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