[N,k,chi] = [136,4,Mod(1,136)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(136, 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("136.1");
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
\(2\)
\(-1\)
\(17\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{3} - 8T_{3}^{2} - 40T_{3} + 176 \)
T3^3 - 8*T3^2 - 40*T3 + 176
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(136))\).
$p$
$F_p(T)$
$2$
\( T^{3} \)
T^3
$3$
\( T^{3} - 8 T^{2} - 40 T + 176 \)
T^3 - 8*T^2 - 40*T + 176
$5$
\( T^{3} - 2 T^{2} - 148 T - 408 \)
T^3 - 2*T^2 - 148*T - 408
$7$
\( T^{3} - 12 T^{2} - 104 T + 272 \)
T^3 - 12*T^2 - 104*T + 272
$11$
\( T^{3} - 72 T^{2} + 952 T + 4752 \)
T^3 - 72*T^2 + 952*T + 4752
$13$
\( T^{3} - 50 T^{2} + 556 T - 1496 \)
T^3 - 50*T^2 + 556*T - 1496
$17$
\( (T - 17)^{3} \)
(T - 17)^3
$19$
\( T^{3} - 124 T^{2} - 1008 T + 151488 \)
T^3 - 124*T^2 - 1008*T + 151488
$23$
\( T^{3} - 60 T^{2} - 23624 T + 1168976 \)
T^3 - 60*T^2 - 23624*T + 1168976
$29$
\( T^{3} + 54 T^{2} - 23156 T - 1826616 \)
T^3 + 54*T^2 - 23156*T - 1826616
$31$
\( T^{3} - 300 T^{2} + 13528 T - 122448 \)
T^3 - 300*T^2 + 13528*T - 122448
$37$
\( T^{3} + 542 T^{2} + 40876 T - 451992 \)
T^3 + 542*T^2 + 40876*T - 451992
$41$
\( T^{3} - 30 T^{2} - 127188 T + 13345816 \)
T^3 - 30*T^2 - 127188*T + 13345816
$43$
\( T^{3} - 52 T^{2} - 34800 T + 2509632 \)
T^3 - 52*T^2 - 34800*T + 2509632
$47$
\( T^{3} - 16 T^{2} - 82560 T + 1737728 \)
T^3 - 16*T^2 - 82560*T + 1737728
$53$
\( T^{3} + 518 T^{2} + \cdots - 97851384 \)
T^3 + 518*T^2 - 213492*T - 97851384
$59$
\( T^{3} - 132 T^{2} - 173040 T + 2838592 \)
T^3 - 132*T^2 - 173040*T + 2838592
$61$
\( T^{3} + 614 T^{2} + \cdots - 115549176 \)
T^3 + 614*T^2 - 280820*T - 115549176
$67$
\( T^{3} + 332 T^{2} + 16944 T + 78912 \)
T^3 + 332*T^2 + 16944*T + 78912
$71$
\( T^{3} + 268 T^{2} + \cdots + 104748848 \)
T^3 + 268*T^2 - 514696*T + 104748848
$73$
\( T^{3} + 578 T^{2} + \cdots + 17940632 \)
T^3 + 578*T^2 - 530900*T + 17940632
$79$
\( T^{3} + 668 T^{2} + \cdots - 976074672 \)
T^3 + 668*T^2 - 1678088*T - 976074672
$83$
\( T^{3} - 876 T^{2} + \cdots + 211499712 \)
T^3 - 876*T^2 - 186608*T + 211499712
$89$
\( T^{3} - 1790 T^{2} + \cdots - 72949736 \)
T^3 - 1790*T^2 + 818796*T - 72949736
$97$
\( T^{3} - 838 T^{2} + \cdots + 60169976 \)
T^3 - 838*T^2 - 96500*T + 60169976
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