[N,k,chi] = [165,6,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, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("165.1");
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
\(3\)
\(1\)
\(5\)
\(-1\)
\(11\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{3} - 2T_{2}^{2} - 25T_{2} + 18 \)
T2^3 - 2*T2^2 - 25*T2 + 18
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(165))\).
$p$
$F_p(T)$
$2$
\( T^{3} - 2 T^{2} - 25 T + 18 \)
T^3 - 2*T^2 - 25*T + 18
$3$
\( (T + 9)^{3} \)
(T + 9)^3
$5$
\( (T - 25)^{3} \)
(T - 25)^3
$7$
\( T^{3} + 68 T^{2} - 15552 T + 247808 \)
T^3 + 68*T^2 - 15552*T + 247808
$11$
\( (T - 121)^{3} \)
(T - 121)^3
$13$
\( T^{3} - 290 T^{2} + \cdots + 132063592 \)
T^3 - 290*T^2 - 455060*T + 132063592
$17$
\( T^{3} - 434 T^{2} + \cdots + 2547052488 \)
T^3 - 434*T^2 - 4200580*T + 2547052488
$19$
\( T^{3} + 2856 T^{2} + \cdots + 137703680 \)
T^3 + 2856*T^2 + 1324816*T + 137703680
$23$
\( T^{3} + 640 T^{2} + \cdots - 15777349632 \)
T^3 + 640*T^2 - 12608768*T - 15777349632
$29$
\( T^{3} + 4538 T^{2} + \cdots - 44413548456 \)
T^3 + 4538*T^2 - 26440804*T - 44413548456
$31$
\( T^{3} + 14968 T^{2} + \cdots + 121645522944 \)
T^3 + 14968*T^2 + 74183808*T + 121645522944
$37$
\( T^{3} + 6190 T^{2} + \cdots + 28013661736 \)
T^3 + 6190*T^2 - 94942100*T + 28013661736
$41$
\( T^{3} + 8926 T^{2} + \cdots + 119305168392 \)
T^3 + 8926*T^2 - 75423556*T + 119305168392
$43$
\( T^{3} + 33592 T^{2} + \cdots - 38997547520 \)
T^3 + 33592*T^2 + 252438928*T - 38997547520
$47$
\( T^{3} + 24640 T^{2} + \cdots - 679997104128 \)
T^3 + 24640*T^2 + 100066240*T - 679997104128
$53$
\( T^{3} + 22934 T^{2} + \cdots - 4393759072056 \)
T^3 + 22934*T^2 - 155251828*T - 4393759072056
$59$
\( T^{3} + 13756 T^{2} + \cdots - 20798004639936 \)
T^3 + 13756*T^2 - 2273938256*T - 20798004639936
$61$
\( T^{3} - 24602 T^{2} + \cdots + 43064794504 \)
T^3 - 24602*T^2 + 104218252*T + 43064794504
$67$
\( T^{3} - 16868 T^{2} + \cdots + 1826752720192 \)
T^3 - 16868*T^2 - 206702672*T + 1826752720192
$71$
\( T^{3} - 4856 T^{2} + \cdots + 34155066048000 \)
T^3 - 4856*T^2 - 3461197888*T + 34155066048000
$73$
\( T^{3} - 1910 T^{2} + \cdots - 163103734088 \)
T^3 - 1910*T^2 - 343684724*T - 163103734088
$79$
\( T^{3} + 36844 T^{2} + \cdots - 70772253539328 \)
T^3 + 36844*T^2 - 4928927232*T - 70772253539328
$83$
\( T^{3} + 48796 T^{2} + \cdots - 70386077185728 \)
T^3 + 48796*T^2 - 2151088976*T - 70386077185728
$89$
\( T^{3} + 188978 T^{2} + \cdots - 16088649675432 \)
T^3 + 188978*T^2 + 8554109420*T - 16088649675432
$97$
\( T^{3} + \cdots - 148869121092488 \)
T^3 - 247526*T^2 + 15492965260*T - 148869121092488
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