[N,k,chi] = [162,6,Mod(1,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.1");
S:= CuspForms(chi, 6);
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
\(2\)
\(-1\)
\(3\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{3} - 54T_{5}^{2} - 4671T_{5} + 215784 \)
T5^3 - 54*T5^2 - 4671*T5 + 215784
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(162))\).
$p$
$F_p(T)$
$2$
\( (T - 4)^{3} \)
(T - 4)^3
$3$
\( T^{3} \)
T^3
$5$
\( T^{3} - 54 T^{2} - 4671 T + 215784 \)
T^3 - 54*T^2 - 4671*T + 215784
$7$
\( T^{3} - 132 T^{2} - 42927 T + 5134078 \)
T^3 - 132*T^2 - 42927*T + 5134078
$11$
\( T^{3} - 315 T^{2} + \cdots + 41768163 \)
T^3 - 315*T^2 - 161865*T + 41768163
$13$
\( T^{3} - 744 T^{2} + \cdots + 384824422 \)
T^3 - 744*T^2 - 670659*T + 384824422
$17$
\( T^{3} - 1449 T^{2} + \cdots + 930192444 \)
T^3 - 1449*T^2 - 500040*T + 930192444
$19$
\( T^{3} - 1131 T^{2} + \cdots - 352455920 \)
T^3 - 1131*T^2 - 1499928*T - 352455920
$23$
\( T^{3} - 3168 T^{2} + \cdots - 425600514 \)
T^3 - 3168*T^2 + 2176281*T - 425600514
$29$
\( T^{3} - 5148 T^{2} + \cdots - 6505725654 \)
T^3 - 5148*T^2 - 12926979*T - 6505725654
$31$
\( T^{3} - 8610 T^{2} + \cdots + 59316561604 \)
T^3 - 8610*T^2 - 1066011*T + 59316561604
$37$
\( T^{3} - 19968 T^{2} + \cdots - 188019064016 \)
T^3 - 19968*T^2 + 119415108*T - 188019064016
$41$
\( T^{3} + 5049 T^{2} + \cdots - 2157363401913 \)
T^3 + 5049*T^2 - 272164833*T - 2157363401913
$43$
\( T^{3} - 31389 T^{2} + \cdots + 513661035961 \)
T^3 - 31389*T^2 + 172368507*T + 513661035961
$47$
\( T^{3} + 12924 T^{2} + \cdots + 84596352750 \)
T^3 + 12924*T^2 - 72375903*T + 84596352750
$53$
\( T^{3} + 48024 T^{2} + \cdots + 1764512817552 \)
T^3 + 48024*T^2 + 557151588*T + 1764512817552
$59$
\( T^{3} + 62955 T^{2} + \cdots - 5778215946243 \)
T^3 + 62955*T^2 + 689925735*T - 5778215946243
$61$
\( T^{3} - 75966 T^{2} + \cdots - 5359653497960 \)
T^3 - 75966*T^2 + 1585078761*T - 5359653497960
$67$
\( T^{3} - 32991 T^{2} + \cdots + 3034793402875 \)
T^3 - 32991*T^2 - 1160180061*T + 3034793402875
$71$
\( T^{3} + 64836 T^{2} + \cdots - 139951336896 \)
T^3 + 64836*T^2 - 82327536*T - 139951336896
$73$
\( T^{3} + 4233 T^{2} + \cdots + 14322358753732 \)
T^3 + 4233*T^2 - 4737509952*T + 14322358753732
$79$
\( T^{3} + \cdots - 115303078320596 \)
T^3 + 89202*T^2 - 327700635*T - 115303078320596
$83$
\( T^{3} + \cdots - 103421607911604 \)
T^3 + 32634*T^2 - 2990259315*T - 103421607911604
$89$
\( T^{3} - 33066 T^{2} + \cdots + 9104584153608 \)
T^3 - 33066*T^2 - 620916948*T + 9104584153608
$97$
\( T^{3} + \cdots - 292114819729997 \)
T^3 + 46245*T^2 - 6556234569*T - 292114819729997
show more
show less