[N,k,chi] = [11,6,Mod(1,11)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(11, 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("11.1");
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
\(11\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{3} - 90T_{2} + 188 \)
T2^3 - 90*T2 + 188
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(11))\).
$p$
$F_p(T)$
$2$
\( T^{3} - 90T + 188 \)
T^3 - 90*T + 188
$3$
\( T^{3} - 34 T^{2} + 217 T + 1212 \)
T^3 - 34*T^2 + 217*T + 1212
$5$
\( T^{3} - 24 T^{2} - 4371 T + 38954 \)
T^3 - 24*T^2 - 4371*T + 38954
$7$
\( T^{3} - 84 T^{2} - 45948 T + 5380448 \)
T^3 - 84*T^2 - 45948*T + 5380448
$11$
\( (T - 121)^{3} \)
(T - 121)^3
$13$
\( T^{3} - 486 T^{2} + \cdots + 164136608 \)
T^3 - 486*T^2 - 346464*T + 164136608
$17$
\( T^{3} - 1086 T^{2} + \cdots + 331752056 \)
T^3 - 1086*T^2 - 1569348*T + 331752056
$19$
\( T^{3} - 1380 T^{2} + \cdots + 57024000 \)
T^3 - 1380*T^2 + 216000*T + 57024000
$23$
\( T^{3} + 3066 T^{2} + \cdots - 17004325928 \)
T^3 + 3066*T^2 - 10315503*T - 17004325928
$29$
\( T^{3} + 3426 T^{2} + \cdots - 4029189120 \)
T^3 + 3426*T^2 + 587712*T - 4029189120
$31$
\( T^{3} + 4098 T^{2} + \cdots + 1094344400 \)
T^3 + 4098*T^2 + 4249425*T + 1094344400
$37$
\( T^{3} - 17724 T^{2} + \cdots + 541788167034 \)
T^3 - 17724*T^2 + 21815085*T + 541788167034
$41$
\( T^{3} - 5994 T^{2} + \cdots + 201929821568 \)
T^3 - 5994*T^2 - 173188800*T + 201929821568
$43$
\( T^{3} + 26208 T^{2} + \cdots - 2443875098544 \)
T^3 + 26208*T^2 + 2680788*T - 2443875098544
$47$
\( T^{3} + 17232 T^{2} + \cdots - 70174939136 \)
T^3 + 17232*T^2 + 1749312*T - 70174939136
$53$
\( T^{3} - 50586 T^{2} + \cdots - 1850911309656 \)
T^3 - 50586*T^2 + 715294812*T - 1850911309656
$59$
\( T^{3} + 3738 T^{2} + \cdots + 7759637437060 \)
T^3 + 3738*T^2 - 851469711*T + 7759637437060
$61$
\( T^{3} - 18486 T^{2} + \cdots + 15233874751008 \)
T^3 - 18486*T^2 - 778919136*T + 15233874751008
$67$
\( T^{3} + \cdots - 147288561330212 \)
T^3 + 47754*T^2 - 3052920807*T - 147288561330212
$71$
\( T^{3} - 39282 T^{2} + \cdots - 1290398551704 \)
T^3 - 39282*T^2 - 979665063*T - 1290398551704
$73$
\( T^{3} - 15426 T^{2} + \cdots - 34539701265952 \)
T^3 - 15426*T^2 - 3656910144*T - 34539701265952
$79$
\( T^{3} - 125148 T^{2} + \cdots + 1279883216320 \)
T^3 - 125148*T^2 + 3891466596*T + 1279883216320
$83$
\( T^{3} + \cdots - 411597824719824 \)
T^3 + 143928*T^2 + 310002228*T - 411597824719824
$89$
\( T^{3} + 106824 T^{2} + \cdots - 90320980174650 \)
T^3 + 106824*T^2 + 922289421*T - 90320980174650
$97$
\( T^{3} - 9684 T^{2} + \cdots - 10221902527106 \)
T^3 - 9684*T^2 - 2112585195*T - 10221902527106
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