[N,k,chi] = [224,4,Mod(1,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, 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("224.1");
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
\(2\)
\(-1\)
\(7\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{3} - 48T_{3} + 56 \)
T3^3 - 48*T3 + 56
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(224))\).
$p$
$F_p(T)$
$2$
\( T^{3} \)
T^3
$3$
\( T^{3} - 48T + 56 \)
T^3 - 48*T + 56
$5$
\( T^{3} + 6 T^{2} - 204 T + 768 \)
T^3 + 6*T^2 - 204*T + 768
$7$
\( (T + 7)^{3} \)
(T + 7)^3
$11$
\( T^{3} - 3456T + 48832 \)
T^3 - 3456*T + 48832
$13$
\( T^{3} + 6 T^{2} - 4284 T - 116816 \)
T^3 + 6*T^2 - 4284*T - 116816
$17$
\( T^{3} + 66 T^{2} - 12660 T - 936424 \)
T^3 + 66*T^2 - 12660*T - 936424
$19$
\( T^{3} + 168 T^{2} - 4128 T - 1148952 \)
T^3 + 168*T^2 - 4128*T - 1148952
$23$
\( T^{3} + 336 T^{2} + 26448 T - 215936 \)
T^3 + 336*T^2 + 26448*T - 215936
$29$
\( T^{3} - 90 T^{2} + 1836 T - 10616 \)
T^3 - 90*T^2 + 1836*T - 10616
$31$
\( T^{3} + 504 T^{2} + 63648 T + 366016 \)
T^3 + 504*T^2 + 63648*T + 366016
$37$
\( T^{3} - 18 T^{2} - 77268 T + 2845928 \)
T^3 - 18*T^2 - 77268*T + 2845928
$41$
\( T^{3} + 450 T^{2} + 11052 T - 7572776 \)
T^3 + 450*T^2 + 11052*T - 7572776
$43$
\( T^{3} - 31296 T + 2128448 \)
T^3 - 31296*T + 2128448
$47$
\( T^{3} + 504 T^{2} + \cdots - 60547648 \)
T^3 + 504*T^2 - 114624*T - 60547648
$53$
\( T^{3} + 78 T^{2} - 331476 T - 67903192 \)
T^3 + 78*T^2 - 331476*T - 67903192
$59$
\( T^{3} - 504 T^{2} + \cdots + 192556616 \)
T^3 - 504*T^2 - 478512*T + 192556616
$61$
\( T^{3} - 498 T^{2} + 69684 T - 2912608 \)
T^3 - 498*T^2 + 69684*T - 2912608
$67$
\( T^{3} - 1008 T^{2} + \cdots - 29986432 \)
T^3 - 1008*T^2 + 317520*T - 29986432
$71$
\( T^{3} + 504 T^{2} + \cdots - 59523072 \)
T^3 + 504*T^2 - 110400*T - 59523072
$73$
\( T^{3} + 234 T^{2} + \cdots - 123555144 \)
T^3 + 234*T^2 - 512052*T - 123555144
$79$
\( T^{3} + 168 T^{2} + \cdots + 41853952 \)
T^3 + 168*T^2 - 945600*T + 41853952
$83$
\( T^{3} - 3024 T^{2} + \cdots - 883723736 \)
T^3 - 3024*T^2 + 2910048*T - 883723736
$89$
\( T^{3} - 246 T^{2} - 108276 T + 3703224 \)
T^3 - 246*T^2 - 108276*T + 3703224
$97$
\( T^{3} + 2514 T^{2} + \cdots - 1004302696 \)
T^3 + 2514*T^2 + 842988*T - 1004302696
show more
show less