[N,k,chi] = [40,10,Mod(1,40)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(40, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("40.1");
S:= CuspForms(chi, 10);
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
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
\( p \)
Sign
\(2\)
\(1\)
\(5\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{3} - 84T_{3}^{2} - 49536T_{3} + 691200 \)
T3^3 - 84*T3^2 - 49536*T3 + 691200
acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(40))\).
$p$
$F_p(T)$
$2$
\( T^{3} \)
T^3
$3$
\( T^{3} - 84 T^{2} - 49536 T + 691200 \)
T^3 - 84*T^2 - 49536*T + 691200
$5$
\( (T - 625)^{3} \)
(T - 625)^3
$7$
\( T^{3} + 5520 T^{2} + \cdots - 117339254144 \)
T^3 + 5520*T^2 - 58842672*T - 117339254144
$11$
\( T^{3} - 5556 T^{2} + \cdots - 46675499449024 \)
T^3 - 5556*T^2 - 4478986896*T - 46675499449024
$13$
\( T^{3} + 83094 T^{2} + \cdots - 10\!\cdots\!88 \)
T^3 + 83094*T^2 - 11736464820*T - 1007468545461688
$17$
\( T^{3} - 367062 T^{2} + \cdots + 17\!\cdots\!00 \)
T^3 - 367062*T^2 - 87258439860*T + 17347013748566200
$19$
\( T^{3} - 1489116 T^{2} + \cdots + 13\!\cdots\!96 \)
T^3 - 1489116*T^2 + 374517012144*T + 130478403486216896
$23$
\( T^{3} + 499920 T^{2} + \cdots - 59\!\cdots\!96 \)
T^3 + 499920*T^2 - 5594704529712*T - 5951731354902637696
$29$
\( T^{3} - 5234682 T^{2} + \cdots + 81\!\cdots\!08 \)
T^3 - 5234682*T^2 - 784452013044*T + 8159417921262643208
$31$
\( T^{3} - 12708912 T^{2} + \cdots - 55\!\cdots\!00 \)
T^3 - 12708912*T^2 + 48812097092160*T - 55900171731714457600
$37$
\( T^{3} - 21724434 T^{2} + \cdots + 28\!\cdots\!04 \)
T^3 - 21724434*T^2 - 103342657572756*T + 2825786294129039569704
$41$
\( T^{3} - 27440478 T^{2} + \cdots - 62\!\cdots\!56 \)
T^3 - 27440478*T^2 + 233646345070380*T - 628613353769854145256
$43$
\( T^{3} + 23218260 T^{2} + \cdots - 20\!\cdots\!92 \)
T^3 + 23218260*T^2 - 1256022211031808*T - 20791009638902617345792
$47$
\( T^{3} + 28701528 T^{2} + \cdots - 19\!\cdots\!24 \)
T^3 + 28701528*T^2 - 667590947413872*T - 19115353220312640001024
$53$
\( T^{3} + 45629982 T^{2} + \cdots + 76\!\cdots\!84 \)
T^3 + 45629982*T^2 - 2358007372929492*T + 76564303514890833384
$59$
\( T^{3} + 268721868 T^{2} + \cdots + 34\!\cdots\!36 \)
T^3 + 268721868*T^2 + 20468715397950000*T + 348741107219499663670336
$61$
\( T^{3} - 155970138 T^{2} + \cdots + 17\!\cdots\!00 \)
T^3 - 155970138*T^2 - 7480658134945140*T + 172490673510567983025800
$67$
\( T^{3} + 526916604 T^{2} + \cdots + 46\!\cdots\!72 \)
T^3 + 526916604*T^2 + 87611183424537600*T + 4677334357339779264508672
$71$
\( T^{3} + 239894424 T^{2} + \cdots - 54\!\cdots\!00 \)
T^3 + 239894424*T^2 - 19718464592365056*T - 5425303310630300663193600
$73$
\( T^{3} - 198362430 T^{2} + \cdots + 89\!\cdots\!24 \)
T^3 - 198362430*T^2 + 932480415973548*T + 896688212352014341718424
$79$
\( T^{3} + 413839728 T^{2} + \cdots - 67\!\cdots\!00 \)
T^3 + 413839728*T^2 + 5593522466359296*T - 6736693919281912494489600
$83$
\( T^{3} - 371949828 T^{2} + \cdots - 65\!\cdots\!36 \)
T^3 - 371949828*T^2 - 222575431721498880*T - 6589623144902819498971136
$89$
\( T^{3} - 754926606 T^{2} + \cdots + 71\!\cdots\!96 \)
T^3 - 754926606*T^2 - 124528404610928916*T + 7172496950578000764382296
$97$
\( T^{3} + 903451002 T^{2} + \cdots + 77\!\cdots\!04 \)
T^3 + 903451002*T^2 + 159195764944371468*T + 7773428463582289734310904
show more
show less