[N,k,chi] = [5,8,Mod(1,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, 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("5.1");
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 \(\beta = 2\sqrt{19}\).
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
\( T_{2}^{2} - 20T_{2} + 24 \)
T2^2 - 20*T2 + 24
acting on \(S_{8}^{\mathrm{new}}(\Gamma_0(5))\).
$p$
$F_p(T)$
$2$
\( T^{2} - 20T + 24 \)
T^2 - 20*T + 24
$3$
\( T^{2} - 20T - 4764 \)
T^2 - 20*T - 4764
$5$
\( (T + 125)^{2} \)
(T + 125)^2
$7$
\( T^{2} + 100T - 235836 \)
T^2 + 100*T - 235836
$11$
\( T^{2} - 4544 T - 6998016 \)
T^2 - 4544*T - 6998016
$13$
\( T^{2} - 3540 T - 24961564 \)
T^2 - 3540*T - 24961564
$17$
\( T^{2} + 27340 T + 80327844 \)
T^2 + 27340*T + 80327844
$19$
\( T^{2} - 38760 T + 367802000 \)
T^2 - 38760*T + 367802000
$23$
\( T^{2} + 124140 T + 3840033636 \)
T^2 + 124140*T + 3840033636
$29$
\( T^{2} + 72260 T - 27652933500 \)
T^2 + 72260*T - 27652933500
$31$
\( T^{2} - 306824 T + 22939401744 \)
T^2 - 306824*T + 22939401744
$37$
\( T^{2} + 123020 T - 45775154396 \)
T^2 + 123020*T - 45775154396
$41$
\( T^{2} - 264364 T - 227722158876 \)
T^2 - 264364*T - 227722158876
$43$
\( T^{2} - 423300 T - 96985991164 \)
T^2 - 423300*T - 96985991164
$47$
\( T^{2} + 105460 T - 154530884316 \)
T^2 + 105460*T - 154530884316
$53$
\( T^{2} + 2391580 T + 1213130224836 \)
T^2 + 2391580*T + 1213130224836
$59$
\( T^{2} + 1120120 T - 3614968086000 \)
T^2 + 1120120*T - 3614968086000
$61$
\( T^{2} - 2257044 T - 672038095516 \)
T^2 - 2257044*T - 672038095516
$67$
\( T^{2} - 4516460 T + 4620664454244 \)
T^2 - 4516460*T + 4620664454244
$71$
\( T^{2} - 621784 T - 275746164336 \)
T^2 - 621784*T - 275746164336
$73$
\( T^{2} - 4569060 T + 1330152816836 \)
T^2 - 4569060*T + 1330152816836
$79$
\( T^{2} - 4333040 T - 12272229720000 \)
T^2 - 4333040*T - 12272229720000
$83$
\( T^{2} + 9793020 T + 5699002341636 \)
T^2 + 9793020*T + 5699002341636
$89$
\( T^{2} - 6025620 T + 1403196358500 \)
T^2 - 6025620*T + 1403196358500
$97$
\( T^{2} - 4609540 T - 18666217374716 \)
T^2 - 4609540*T - 18666217374716
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