[N,k,chi] = [320,10,Mod(1,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, 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("320.1");
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 subspace can be constructed as the kernel of the linear operator
\( T_{3}^{4} - 47248T_{3}^{2} + 411278400 \)
T3^4 - 47248*T3^2 + 411278400
acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(320))\).
$p$
$F_p(T)$
$2$
\( T^{4} \)
T^4
$3$
\( T^{4} - 47248 T^{2} + \cdots + 411278400 \)
T^4 - 47248*T^2 + 411278400
$5$
\( (T + 625)^{4} \)
(T + 625)^4
$7$
\( T^{4} - 88336528 T^{2} + \cdots + 18\!\cdots\!00 \)
T^4 - 88336528*T^2 + 1807232733633600
$11$
\( T^{4} - 2764259392 T^{2} + \cdots + 43\!\cdots\!00 \)
T^4 - 2764259392*T^2 + 439312535979033600
$13$
\( (T^{2} - 66372 T - 10047638908)^{2} \)
(T^2 - 66372*T - 10047638908)^2
$17$
\( (T^{2} + 391420 T - 19587639804)^{2} \)
(T^2 + 391420*T - 19587639804)^2
$19$
\( T^{4} - 804604403200 T^{2} + \cdots + 43\!\cdots\!00 \)
T^4 - 804604403200*T^2 + 43659641139618816000000
$23$
\( T^{4} - 800031279248 T^{2} + \cdots + 15\!\cdots\!00 \)
T^4 - 800031279248*T^2 + 156680132728096207297600
$29$
\( (T^{2} - 4492724 T - 20395982253660)^{2} \)
(T^2 - 4492724*T - 20395982253660)^2
$31$
\( T^{4} - 81400225018432 T^{2} + \cdots + 78\!\cdots\!00 \)
T^4 - 81400225018432*T^2 + 788797166797009693550822400
$37$
\( (T^{2} + 13169708 T - 162155268204060)^{2} \)
(T^2 + 13169708*T - 162155268204060)^2
$41$
\( (T^{2} + 20910588 T - 52418231901180)^{2} \)
(T^2 + 20910588*T - 52418231901180)^2
$43$
\( T^{4} - 691305167698192 T^{2} + \cdots + 78\!\cdots\!00 \)
T^4 - 691305167698192*T^2 + 78043022378379917253968040000
$47$
\( T^{4} + \cdots + 12\!\cdots\!00 \)
T^4 - 3503666661663888*T^2 + 1283326950589965958992478862400
$53$
\( (T^{2} + 46634828 T - 33\!\cdots\!04)^{2} \)
(T^2 + 46634828*T - 3353439495719004)^2
$59$
\( T^{4} + \cdots + 16\!\cdots\!00 \)
T^4 - 18730836635715328*T^2 + 1608750090333312452280045158400
$61$
\( (T^{2} - 55091012 T - 90\!\cdots\!80)^{2} \)
(T^2 - 55091012*T - 9054010485120380)^2
$67$
\( T^{4} + \cdots + 58\!\cdots\!00 \)
T^4 - 61628151502485648*T^2 + 583807376839399997781493173902400
$71$
\( T^{4} + \cdots + 14\!\cdots\!00 \)
T^4 - 1017936622914112*T^2 + 142784463572715881361947673600
$73$
\( (T^{2} + 281793420 T + 19\!\cdots\!04)^{2} \)
(T^2 + 281793420*T + 19842421625408804)^2
$79$
\( T^{4} + \cdots + 15\!\cdots\!00 \)
T^4 - 302610358143527168*T^2 + 15826661003196724406928369500569600
$83$
\( T^{4} + \cdots + 54\!\cdots\!00 \)
T^4 - 472481537155508368*T^2 + 54769966548911319403150955110440000
$89$
\( (T^{2} + 10176620 T - 13\!\cdots\!00)^{2} \)
(T^2 + 10176620*T - 139364969664390300)^2
$97$
\( (T^{2} + 242496764 T + 18\!\cdots\!24)^{2} \)
(T^2 + 242496764*T + 1883881088376324)^2
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