[N,k,chi] = [1296,4,Mod(1,1296)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1296, 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("1296.1");
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
\(2\)
\(1\)
\(3\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{4} + 8T_{5}^{3} - 222T_{5}^{2} - 376T_{5} + 6961 \)
T5^4 + 8*T5^3 - 222*T5^2 - 376*T5 + 6961
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1296))\).
$p$
$F_p(T)$
$2$
\( T^{4} \)
T^4
$3$
\( T^{4} \)
T^4
$5$
\( T^{4} + 8 T^{3} - 222 T^{2} + \cdots + 6961 \)
T^4 + 8*T^3 - 222*T^2 - 376*T + 6961
$7$
\( T^{4} - 552 T^{2} - 3456 T + 1296 \)
T^4 - 552*T^2 - 3456*T + 1296
$11$
\( T^{4} - 8 T^{3} - 1560 T^{2} + \cdots + 61072 \)
T^4 - 8*T^3 - 1560*T^2 + 6304*T + 61072
$13$
\( T^{4} - 4 T^{3} - 2274 T^{2} + \cdots + 1237417 \)
T^4 - 4*T^3 - 2274*T^2 + 3404*T + 1237417
$17$
\( T^{4} + 16 T^{3} - 7782 T^{2} + \cdots + 14319721 \)
T^4 + 16*T^3 - 7782*T^2 - 69680*T + 14319721
$19$
\( T^{4} + 80 T^{3} - 10824 T^{2} + \cdots + 31790992 \)
T^4 + 80*T^3 - 10824*T^2 - 530368*T + 31790992
$23$
\( T^{4} - 200 T^{3} + \cdots + 48919312 \)
T^4 - 200*T^3 - 10104*T^2 + 1100320*T + 48919312
$29$
\( T^{4} + 216 T^{3} + \cdots + 54863217 \)
T^4 + 216*T^3 - 4638*T^2 - 1735848*T + 54863217
$31$
\( T^{4} + 80 T^{3} - 15936 T^{2} + \cdots + 48805888 \)
T^4 + 80*T^3 - 15936*T^2 - 342016*T + 48805888
$37$
\( T^{4} + 276 T^{3} + \cdots + 948334041 \)
T^4 + 276*T^3 - 99282*T^2 - 23154588*T + 948334041
$41$
\( T^{4} + 384 T^{3} + \cdots - 2045323008 \)
T^4 + 384*T^3 - 17760*T^2 - 21141504*T - 2045323008
$43$
\( T^{4} + 160 T^{3} + \cdots + 513055504 \)
T^4 + 160*T^3 - 202920*T^2 - 1524224*T + 513055504
$47$
\( T^{4} - 768 T^{3} + \cdots - 1142228736 \)
T^4 - 768*T^3 + 157344*T^2 - 847872*T - 1142228736
$53$
\( T^{4} + 944 T^{3} + \cdots - 22310316032 \)
T^4 + 944*T^3 + 84288*T^2 - 112215040*T - 22310316032
$59$
\( T^{4} - 992 T^{3} + \cdots + 593268736 \)
T^4 - 992*T^3 + 30336*T^2 + 83089408*T + 593268736
$61$
\( T^{4} + 548 T^{3} + \cdots + 104164416841 \)
T^4 + 548*T^3 - 575106*T^2 - 177955180*T + 104164416841
$67$
\( T^{4} + 464 T^{3} + \cdots - 30700073072 \)
T^4 + 464*T^3 - 704328*T^2 - 359901376*T - 30700073072
$71$
\( T^{4} - 1720 T^{3} + \cdots - 9807661424 \)
T^4 - 1720*T^3 + 880872*T^2 - 110047648*T - 9807661424
$73$
\( T^{4} + 764 T^{3} + \cdots - 194677777919 \)
T^4 + 764*T^3 - 912378*T^2 - 951038212*T - 194677777919
$79$
\( T^{4} + 688 T^{3} + \cdots + 320004558736 \)
T^4 + 688*T^3 - 1761864*T^2 - 1127611712*T + 320004558736
$83$
\( T^{4} - 2128 T^{3} + \cdots + 6134511616 \)
T^4 - 2128*T^3 + 1236288*T^2 - 164967424*T + 6134511616
$89$
\( T^{4} + 2112 T^{3} + \cdots - 1312975087623 \)
T^4 + 2112*T^3 - 109206*T^2 - 2534079168*T - 1312975087623
$97$
\( T^{4} + 1816 T^{3} + \cdots + 2989754128 \)
T^4 + 1816*T^3 - 1073832*T^2 - 2084846240*T + 2989754128
show more
show less