[N,k,chi] = [165,4,Mod(1,165)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(165, 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("165.1");
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
\(3\)
\(1\)
\(5\)
\(-1\)
\(11\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{3} - T_{2}^{2} - 9T_{2} + 5 \)
T2^3 - T2^2 - 9*T2 + 5
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(165))\).
$p$
$F_p(T)$
$2$
\( T^{3} - T^{2} - 9T + 5 \)
T^3 - T^2 - 9*T + 5
$3$
\( (T + 3)^{3} \)
(T + 3)^3
$5$
\( (T - 5)^{3} \)
(T - 5)^3
$7$
\( T^{3} + 16 T^{2} - 752 T - 5808 \)
T^3 + 16*T^2 - 752*T - 5808
$11$
\( (T + 11)^{3} \)
(T + 11)^3
$13$
\( T^{3} + 42 T^{2} - 5228 T - 137416 \)
T^3 + 42*T^2 - 5228*T - 137416
$17$
\( T^{3} + 34 T^{2} - 4660 T - 179064 \)
T^3 + 34*T^2 - 4660*T - 179064
$19$
\( T^{3} + 280 T^{2} + 18624 T - 97056 \)
T^3 + 280*T^2 + 18624*T - 97056
$23$
\( T^{3} + 112 T^{2} - 17024 T - 1916288 \)
T^3 + 112*T^2 - 17024*T - 1916288
$29$
\( T^{3} + 290 T^{2} - 26500 T - 9251496 \)
T^3 + 290*T^2 - 26500*T - 9251496
$31$
\( T^{3} + 392 T^{2} + 32160 T - 316800 \)
T^3 + 392*T^2 + 32160*T - 316800
$37$
\( T^{3} - 570 T^{2} + 60940 T + 1039624 \)
T^3 - 570*T^2 + 60940*T + 1039624
$41$
\( T^{3} + 662 T^{2} + \cdots - 68561784 \)
T^3 + 662*T^2 - 55908*T - 68561784
$43$
\( T^{3} + 68 T^{2} - 227376 T - 20491056 \)
T^3 + 68*T^2 - 227376*T - 20491056
$47$
\( T^{3} - 264 T^{2} + \cdots - 14121600 \)
T^3 - 264*T^2 - 164576*T - 14121600
$53$
\( T^{3} + 94 T^{2} - 57812 T - 2403992 \)
T^3 + 94*T^2 - 57812*T - 2403992
$59$
\( T^{3} + 612 T^{2} + \cdots - 162128320 \)
T^3 + 612*T^2 - 424784*T - 162128320
$61$
\( T^{3} + 582 T^{2} + \cdots - 21355000 \)
T^3 + 582*T^2 + 20044*T - 21355000
$67$
\( T^{3} - 940 T^{2} + \cdots + 394498240 \)
T^3 - 940*T^2 - 389488*T + 394498240
$71$
\( T^{3} + 1616 T^{2} + \cdots + 40198784 \)
T^3 + 1616*T^2 + 671200*T + 40198784
$73$
\( T^{3} - 738 T^{2} + \cdots - 12046264 \)
T^3 - 738*T^2 + 168868*T - 12046264
$79$
\( T^{3} - 124 T^{2} + \cdots + 26871328 \)
T^3 - 124*T^2 - 185872*T + 26871328
$83$
\( T^{3} + 1232 T^{2} + \cdots - 15656400 \)
T^3 + 1232*T^2 + 293160*T - 15656400
$89$
\( T^{3} - 838 T^{2} + \cdots + 831946232 \)
T^3 - 838*T^2 - 1004532*T + 831946232
$97$
\( T^{3} + 90 T^{2} + \cdots - 924170696 \)
T^3 + 90*T^2 - 2296340*T - 924170696
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