[N,k,chi] = [462,6,Mod(1,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.1");
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
\(2\)
\(-1\)
\(3\)
\(1\)
\(7\)
\(1\)
\(11\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{3} + 56T_{5}^{2} - 2851T_{5} - 72806 \)
T5^3 + 56*T5^2 - 2851*T5 - 72806
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(462))\).
$p$
$F_p(T)$
$2$
\( (T - 4)^{3} \)
(T - 4)^3
$3$
\( (T + 9)^{3} \)
(T + 9)^3
$5$
\( T^{3} + 56 T^{2} - 2851 T - 72806 \)
T^3 + 56*T^2 - 2851*T - 72806
$7$
\( (T + 49)^{3} \)
(T + 49)^3
$11$
\( (T + 121)^{3} \)
(T + 121)^3
$13$
\( T^{3} + 552 T^{2} + \cdots - 41954486 \)
T^3 + 552*T^2 - 46515*T - 41954486
$17$
\( T^{3} + 778 T^{2} + \cdots - 1189290768 \)
T^3 + 778*T^2 - 1415376*T - 1189290768
$19$
\( T^{3} + 34 T^{2} + \cdots + 1076826276 \)
T^3 + 34*T^2 - 2267411*T + 1076826276
$23$
\( T^{3} - 872 T^{2} + \cdots + 34291256000 \)
T^3 - 872*T^2 - 18267340*T + 34291256000
$29$
\( T^{3} - 4752 T^{2} + \cdots + 91376488442 \)
T^3 - 4752*T^2 - 19687611*T + 91376488442
$31$
\( T^{3} - 3116 T^{2} + \cdots + 64837779776 \)
T^3 - 3116*T^2 - 20384536*T + 64837779776
$37$
\( T^{3} - 4768 T^{2} + \cdots + 130024130874 \)
T^3 - 4768*T^2 - 46775355*T + 130024130874
$41$
\( T^{3} + 7166 T^{2} + \cdots - 71994789696 \)
T^3 + 7166*T^2 - 19960656*T - 71994789696
$43$
\( T^{3} - 10508 T^{2} + \cdots + 226075983344 \)
T^3 - 10508*T^2 - 124259212*T + 226075983344
$47$
\( T^{3} - 7782 T^{2} + \cdots - 593934816200 \)
T^3 - 7782*T^2 - 191872875*T - 593934816200
$53$
\( T^{3} - 27742 T^{2} + \cdots + 2245924957512 \)
T^3 - 27742*T^2 + 33339844*T + 2245924957512
$59$
\( T^{3} - 3850 T^{2} + \cdots - 251464184100 \)
T^3 - 3850*T^2 - 140803979*T - 251464184100
$61$
\( T^{3} - 50106 T^{2} + \cdots + 21398159861960 \)
T^3 - 50106*T^2 - 111601812*T + 21398159861960
$67$
\( T^{3} - 110686 T^{2} + \cdots + 52537797876 \)
T^3 - 110686*T^2 + 3054668509*T + 52537797876
$71$
\( T^{3} - 105720 T^{2} + \cdots + 24201305600000 \)
T^3 - 105720*T^2 + 1990836000*T + 24201305600000
$73$
\( T^{3} - 74544 T^{2} + \cdots - 13207717817050 \)
T^3 - 74544*T^2 + 1753245909*T - 13207717817050
$79$
\( T^{3} - 67952 T^{2} + \cdots + 9666171542016 \)
T^3 - 67952*T^2 + 468734800*T + 9666171542016
$83$
\( T^{3} - 46216 T^{2} + \cdots + 13636328729760 \)
T^3 - 46216*T^2 - 9320500712*T + 13636328729760
$89$
\( T^{3} + \cdots + 292611013505880 \)
T^3 - 124750*T^2 - 4462603796*T + 292611013505880
$97$
\( T^{3} + 54110 T^{2} + \cdots - 10\!\cdots\!00 \)
T^3 + 54110*T^2 - 14887603164*T - 1003253480934600
show more
show less