[N,k,chi] = [25,8,Mod(1,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.1");
S:= CuspForms(chi, 8);
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 \(\beta = \frac{1}{2}(1 + \sqrt{649})\).
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
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{2} - 15T_{2} - 106 \)
T2^2 - 15*T2 - 106
acting on \(S_{8}^{\mathrm{new}}(\Gamma_0(25))\).
$p$
$F_p(T)$
$2$
\( T^{2} - 15T - 106 \)
T^2 - 15*T - 106
$3$
\( T^{2} - 40T - 249 \)
T^2 - 40*T - 249
$5$
\( T^{2} \)
T^2
$7$
\( T^{2} + 600 T - 1054836 \)
T^2 + 600*T - 1054836
$11$
\( T^{2} - 4344 T - 5423041 \)
T^2 - 4344*T - 5423041
$13$
\( T^{2} - 17680 T + 51136816 \)
T^2 - 17680*T + 51136816
$17$
\( T^{2} - 6870 T - 68614471 \)
T^2 - 6870*T - 68614471
$19$
\( T^{2} - 18200 T - 117098225 \)
T^2 - 18200*T - 117098225
$23$
\( T^{2} - 21120 T - 7241627844 \)
T^2 - 21120*T - 7241627844
$29$
\( T^{2} - 55800 T - 27320953600 \)
T^2 - 55800*T - 27320953600
$31$
\( T^{2} + 301776 T + 19481626044 \)
T^2 + 301776*T + 19481626044
$37$
\( T^{2} - 609860 T + 72425629684 \)
T^2 - 609860*T + 72425629684
$41$
\( T^{2} + 108486 T + 2293303049 \)
T^2 + 108486*T + 2293303049
$43$
\( T^{2} - 966400 T + 168009863536 \)
T^2 - 966400*T + 168009863536
$47$
\( T^{2} - 1787880 T + 768835854224 \)
T^2 - 1787880*T + 768835854224
$53$
\( T^{2} - 130740 T - 310528480924 \)
T^2 - 130740*T - 310528480924
$59$
\( T^{2} - 2067600 T - 174052062400 \)
T^2 - 2067600*T - 174052062400
$61$
\( T^{2} - 582044 T - 8129212445516 \)
T^2 - 582044*T - 8129212445516
$67$
\( T^{2} - 255720 T - 858879415521 \)
T^2 - 255720*T - 858879415521
$71$
\( T^{2} + 4728216 T + 5183381635664 \)
T^2 + 4728216*T + 5183381635664
$73$
\( T^{2} + 1339430 T - 708123554519 \)
T^2 + 1339430*T - 708123554519
$79$
\( T^{2} + 7186200 T + 11646468081900 \)
T^2 + 7186200*T + 11646468081900
$83$
\( T^{2} - 12049560 T + 35517015006471 \)
T^2 - 12049560*T + 35517015006471
$89$
\( T^{2} + 5990850 T - 22736713427775 \)
T^2 + 5990850*T - 22736713427775
$97$
\( T^{2} + 17120020 T + 70829616805924 \)
T^2 + 17120020*T + 70829616805924
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