[N,k,chi] = [16,22,Mod(1,16)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16.1");
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
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = 192\sqrt{358549}\).
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.
Refresh table
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{2} - 105432T_{3} - 10438573680 \)
T3^2 - 105432*T3 - 10438573680
acting on \(S_{22}^{\mathrm{new}}(\Gamma_0(16))\).
$p$
$F_p(T)$
$2$
\( T^{2} \)
T^2
$3$
\( T^{2} - 105432 T - 10438573680 \)
T^2 - 105432*T - 10438573680
$5$
\( T^{2} - 2108140 T - 4175956569500 \)
T^2 - 2108140*T - 4175956569500
$7$
\( T^{2} + 444771792 T - 18\!\cdots\!08 \)
T^2 + 444771792*T - 186151101783772608
$11$
\( T^{2} + 53806403320 T - 29\!\cdots\!96 \)
T^2 + 53806403320*T - 2949636775676283866096
$13$
\( T^{2} + 490366676932 T - 18\!\cdots\!48 \)
T^2 + 490366676932*T - 185929556202944946740348
$17$
\( T^{2} + 6593864672092 T - 16\!\cdots\!00 \)
T^2 + 6593864672092*T - 1602407921425784196525500
$19$
\( T^{2} + 19302397925320 T - 16\!\cdots\!36 \)
T^2 + 19302397925320*T - 1681097716586671471373905136
$23$
\( T^{2} - 409737865776272 T + 30\!\cdots\!72 \)
T^2 - 409737865776272*T + 30186185006642609312893252672
$29$
\( T^{2} + \cdots - 56\!\cdots\!84 \)
T^2 + 2404787522145060*T - 5663928219024679950923335530684
$31$
\( T^{2} + \cdots + 14\!\cdots\!20 \)
T^2 - 8689907170559168*T + 14566591001721269452501850629120
$37$
\( T^{2} + \cdots - 32\!\cdots\!16 \)
T^2 + 2186204096251860*T - 32989770483110090500242805042716
$41$
\( T^{2} + \cdots + 11\!\cdots\!08 \)
T^2 - 68178038573558676*T + 1159642763896012565482481814487908
$43$
\( T^{2} + \cdots + 96\!\cdots\!48 \)
T^2 + 264529652266004024*T + 9659744324730488991997865471884048
$47$
\( T^{2} + \cdots - 25\!\cdots\!44 \)
T^2 + 426494411558622432*T - 25649066091790616845331352824319744
$53$
\( T^{2} + \cdots + 22\!\cdots\!56 \)
T^2 + 3055980275589518132*T + 2222195850765831583916673906815086756
$59$
\( T^{2} + \cdots - 55\!\cdots\!12 \)
T^2 + 783424997522814424*T - 551756883532585725322258639565555312
$61$
\( T^{2} + \cdots + 56\!\cdots\!40 \)
T^2 + 7177279049078597092*T + 5679690236541051054236973766791097540
$67$
\( T^{2} + \cdots - 10\!\cdots\!28 \)
T^2 + 16674123174011538088*T - 10486428147741971428724879642139913328
$71$
\( T^{2} + \cdots - 68\!\cdots\!40 \)
T^2 + 9448263149848716368*T - 684458150530562171163887427896820079040
$73$
\( T^{2} + \cdots - 36\!\cdots\!48 \)
T^2 + 11586140334503007532*T - 3654811955551608188375239537342040043548
$79$
\( T^{2} + \cdots + 15\!\cdots\!80 \)
T^2 - 85280702218715897824*T + 151847467557034910477594457634623258880
$83$
\( T^{2} + \cdots + 31\!\cdots\!48 \)
T^2 - 381814622040086245816*T + 31815724933370318859011604250905718271248
$89$
\( T^{2} + \cdots - 21\!\cdots\!56 \)
T^2 + 59742932430695979660*T - 21937925494731048892003453235942283432156
$97$
\( T^{2} + \cdots + 15\!\cdots\!36 \)
T^2 - 783394660926711950788*T + 153105130079120052383219207516307789455236
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