[N,k,chi] = [232,4,Mod(1,232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(232, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("232.1");
S:= CuspForms(chi, 4);
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
\(2\)
\(1\)
\(29\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{3} - 6T_{3}^{2} - 45T_{3} + 158 \)
T3^3 - 6*T3^2 - 45*T3 + 158
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(232))\).
$p$
$F_p(T)$
$2$
\( T^{3} \)
T^3
$3$
\( T^{3} - 6 T^{2} - 45 T + 158 \)
T^3 - 6*T^2 - 45*T + 158
$5$
\( T^{3} - 4 T^{2} - 175 T + 386 \)
T^3 - 4*T^2 - 175*T + 386
$7$
\( T^{3} - 16 T^{2} - 812 T + 13456 \)
T^3 - 16*T^2 - 812*T + 13456
$11$
\( T^{3} + 2 T^{2} - 301 T - 106 \)
T^3 + 2*T^2 - 301*T - 106
$13$
\( T^{3} - 28 T^{2} - 3999 T + 137518 \)
T^3 - 28*T^2 - 3999*T + 137518
$17$
\( T^{3} + 66 T^{2} - 184 T - 1696 \)
T^3 + 66*T^2 - 184*T - 1696
$19$
\( T^{3} + 66 T^{2} - 9616 T - 393632 \)
T^3 + 66*T^2 - 9616*T - 393632
$23$
\( T^{3} - 176 T^{2} + 8192 T - 106688 \)
T^3 - 176*T^2 + 8192*T - 106688
$29$
\( (T + 29)^{3} \)
(T + 29)^3
$31$
\( T^{3} + 190 T^{2} - 54433 T - 9505226 \)
T^3 + 190*T^2 - 54433*T - 9505226
$37$
\( T^{3} - 442 T^{2} + \cdots + 10323328 \)
T^3 - 442*T^2 + 7392*T + 10323328
$41$
\( T^{3} - 1162 T^{2} + \cdots - 53735864 \)
T^3 - 1162*T^2 + 438636*T - 53735864
$43$
\( T^{3} - 30 T^{2} - 81277 T - 8035162 \)
T^3 - 30*T^2 - 81277*T - 8035162
$47$
\( T^{3} + 738 T^{2} + \cdots + 10647458 \)
T^3 + 738*T^2 + 159287*T + 10647458
$53$
\( T^{3} - 312 T^{2} - 97471 T - 4921082 \)
T^3 - 312*T^2 - 97471*T - 4921082
$59$
\( T^{3} - 44 T^{2} - 23280 T - 849664 \)
T^3 - 44*T^2 - 23280*T - 849664
$61$
\( T^{3} - 54 T^{2} - 559656 T + 87366816 \)
T^3 - 54*T^2 - 559656*T + 87366816
$67$
\( T^{3} + 116 T^{2} + \cdots + 19023808 \)
T^3 + 116*T^2 - 182096*T + 19023808
$71$
\( T^{3} + 1200 T^{2} + \cdots + 44065376 \)
T^3 + 1200*T^2 + 437756*T + 44065376
$73$
\( T^{3} + 1118 T^{2} + \cdots - 19620512 \)
T^3 + 1118*T^2 + 147744*T - 19620512
$79$
\( T^{3} + 2262 T^{2} + \cdots + 199598902 \)
T^3 + 2262*T^2 + 1396799*T + 199598902
$83$
\( T^{3} + 1804 T^{2} + \cdots - 652294144 \)
T^3 + 1804*T^2 + 124048*T - 652294144
$89$
\( T^{3} - 1578 T^{2} + \cdots + 1024346504 \)
T^3 - 1578*T^2 - 475636*T + 1024346504
$97$
\( T^{3} - 1450 T^{2} + \cdots + 1820417096 \)
T^3 - 1450*T^2 - 1209748*T + 1820417096
show more
show less