[N,k,chi] = [224,6,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, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.1");
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
sage: f.q_expansion() # note that sage often uses an isomorphic number field
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \sqrt{61}\).
We also show the integral \(q\)-expansion of the trace form .
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
\( T_{3}^{2} - 14T_{3} - 12 \)
T3^2 - 14*T3 - 12
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(224))\).
$p$
$F_p(T)$
$2$
\( T^{2} \)
T^2
$3$
\( T^{2} - 14T - 12 \)
T^2 - 14*T - 12
$5$
\( T^{2} - 34T - 2700 \)
T^2 - 34*T - 2700
$7$
\( (T - 49)^{2} \)
(T - 49)^2
$11$
\( T^{2} + 420T - 84976 \)
T^2 + 420*T - 84976
$13$
\( T^{2} + 490T - 86436 \)
T^2 + 490*T - 86436
$17$
\( T^{2} + 1056 T + 266828 \)
T^2 + 1056*T + 266828
$19$
\( T^{2} + 1246 T - 3333420 \)
T^2 + 1246*T - 3333420
$23$
\( T^{2} - 504T + 47888 \)
T^2 - 504*T + 47888
$29$
\( T^{2} + 3904 T - 14374772 \)
T^2 + 3904*T - 14374772
$31$
\( T^{2} + 2044 T - 24097520 \)
T^2 + 2044*T - 24097520
$37$
\( T^{2} + 7488 T + 14005580 \)
T^2 + 7488*T + 14005580
$41$
\( T^{2} - 7832 T - 63108260 \)
T^2 - 7832*T - 63108260
$43$
\( T^{2} + 10332 T - 45786544 \)
T^2 + 10332*T - 45786544
$47$
\( T^{2} + 41972 T + 396339696 \)
T^2 + 41972*T + 396339696
$53$
\( T^{2} - 32812 T - 171589148 \)
T^2 - 32812*T - 171589148
$59$
\( T^{2} + 48398 T + 421726020 \)
T^2 + 48398*T + 421726020
$61$
\( T^{2} + 718 T - 11734460 \)
T^2 + 718*T - 11734460
$67$
\( T^{2} + 12824 T - 792171632 \)
T^2 + 12824*T - 792171632
$71$
\( T^{2} + 103992 T + 2694018240 \)
T^2 + 103992*T + 2694018240
$73$
\( T^{2} + 54100 T - 1049693676 \)
T^2 + 54100*T - 1049693676
$79$
\( T^{2} + 64568 T + 967369152 \)
T^2 + 64568*T + 967369152
$83$
\( T^{2} - 47810 T + 554507556 \)
T^2 - 47810*T + 554507556
$89$
\( T^{2} + 17388 T - 12657841308 \)
T^2 + 17388*T - 12657841308
$97$
\( T^{2} + 97296 T + 62455628 \)
T^2 + 97296*T + 62455628
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