[N,k,chi] = [966,4,Mod(1,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, 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("966.1");
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
\(2\)
\(-1\)
\(3\)
\(1\)
\(7\)
\(1\)
\(23\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{3} - 5T_{5}^{2} - 191T_{5} + 878 \)
T5^3 - 5*T5^2 - 191*T5 + 878
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(966))\).
$p$
$F_p(T)$
$2$
\( (T - 2)^{3} \)
(T - 2)^3
$3$
\( (T + 3)^{3} \)
(T + 3)^3
$5$
\( T^{3} - 5 T^{2} - 191 T + 878 \)
T^3 - 5*T^2 - 191*T + 878
$7$
\( (T + 7)^{3} \)
(T + 7)^3
$11$
\( T^{3} + 56 T^{2} + 843 T + 1624 \)
T^3 + 56*T^2 + 843*T + 1624
$13$
\( T^{3} - 29 T^{2} - 967 T + 9196 \)
T^3 - 29*T^2 - 967*T + 9196
$17$
\( T^{3} - 28 T^{2} - 10521 T + 43912 \)
T^3 - 28*T^2 - 10521*T + 43912
$19$
\( T^{3} + 18 T^{2} - 15841 T - 568942 \)
T^3 + 18*T^2 - 15841*T - 568942
$23$
\( (T + 23)^{3} \)
(T + 23)^3
$29$
\( T^{3} + 242 T^{2} - 19169 T - 5522006 \)
T^3 + 242*T^2 - 19169*T - 5522006
$31$
\( T^{3} + 86 T^{2} - 35477 T + 1384186 \)
T^3 + 86*T^2 - 35477*T + 1384186
$37$
\( T^{3} + 70 T^{2} - 3253 T - 191606 \)
T^3 + 70*T^2 - 3253*T - 191606
$41$
\( T^{3} + 402 T^{2} + \cdots - 10246778 \)
T^3 + 402*T^2 - 4453*T - 10246778
$43$
\( T^{3} + 553 T^{2} + 90539 T + 3778276 \)
T^3 + 553*T^2 + 90539*T + 3778276
$47$
\( T^{3} + 368 T^{2} + 7024 T - 669944 \)
T^3 + 368*T^2 + 7024*T - 669944
$53$
\( T^{3} - 23 T^{2} - 23259 T + 1462334 \)
T^3 - 23*T^2 - 23259*T + 1462334
$59$
\( T^{3} + 861 T^{2} + 177201 T + 3166884 \)
T^3 + 861*T^2 + 177201*T + 3166884
$61$
\( T^{3} + 311 T^{2} + \cdots - 67548734 \)
T^3 + 311*T^2 - 323147*T - 67548734
$67$
\( T^{3} + 215 T^{2} + \cdots - 105321548 \)
T^3 + 215*T^2 - 357471*T - 105321548
$71$
\( T^{3} - 121 T^{2} - 27289 T - 978964 \)
T^3 - 121*T^2 - 27289*T - 978964
$73$
\( T^{3} + 588 T^{2} + \cdots - 464169806 \)
T^3 + 588*T^2 - 837955*T - 464169806
$79$
\( T^{3} + 1418 T^{2} + \cdots + 45422608 \)
T^3 + 1418*T^2 + 472789*T + 45422608
$83$
\( T^{3} + 352 T^{2} + \cdots + 93148418 \)
T^3 + 352*T^2 - 595235*T + 93148418
$89$
\( T^{3} - 1275 T^{2} + \cdots + 421896500 \)
T^3 - 1275*T^2 - 168775*T + 421896500
$97$
\( T^{3} + 602 T^{2} + \cdots - 254189276 \)
T^3 + 602*T^2 - 2139311*T - 254189276
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