[N,k,chi] = [20,8,Mod(1,20)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(20, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("20.1");
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 \(\beta = 2\sqrt{1129}\).
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
\(2\)
\(-1\)
\(5\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{2} + 20T_{3} - 4416 \)
T3^2 + 20*T3 - 4416
acting on \(S_{8}^{\mathrm{new}}(\Gamma_0(20))\).
$p$
$F_p(T)$
$2$
\( T^{2} \)
T^2
$3$
\( T^{2} + 20T - 4416 \)
T^2 + 20*T - 4416
$5$
\( (T - 125)^{2} \)
(T - 125)^2
$7$
\( T^{2} - 1660 T + 323104 \)
T^2 - 1660*T + 323104
$11$
\( T^{2} - 3600 T - 33339600 \)
T^2 - 3600*T - 33339600
$13$
\( T^{2} - 13180 T + 37575364 \)
T^2 - 13180*T + 37575364
$17$
\( T^{2} - 5460 T - 981659484 \)
T^2 - 5460*T - 981659484
$19$
\( T^{2} + 40472 T + 263177296 \)
T^2 + 40472*T + 263177296
$23$
\( T^{2} + 41820 T + 419304096 \)
T^2 + 41820*T + 419304096
$29$
\( T^{2} - 118668 T + 2935249956 \)
T^2 - 118668*T + 2935249956
$31$
\( T^{2} + 115928 T - 41450184704 \)
T^2 + 115928*T - 41450184704
$37$
\( T^{2} - 306940 T - 69364995836 \)
T^2 - 306940*T - 69364995836
$41$
\( T^{2} + 353148 T - 75487736124 \)
T^2 + 353148*T - 75487736124
$43$
\( T^{2} - 1215340 T + 323163388000 \)
T^2 - 1215340*T + 323163388000
$47$
\( T^{2} + 2068500 T + 1069567347456 \)
T^2 + 2068500*T + 1069567347456
$53$
\( T^{2} - 1400460 T - 323963254044 \)
T^2 - 1400460*T - 323963254044
$59$
\( T^{2} + 1992504 T + 500302949904 \)
T^2 + 1992504*T + 500302949904
$61$
\( T^{2} + 1678676 T - 5384698256156 \)
T^2 + 1678676*T - 5384698256156
$67$
\( T^{2} - 3663940 T + 403671776224 \)
T^2 - 3663940*T + 403671776224
$71$
\( T^{2} - 1794936 T - 761950469376 \)
T^2 - 1794936*T - 761950469376
$73$
\( T^{2} - 5062180 T - 2578241352956 \)
T^2 - 5062180*T - 2578241352956
$79$
\( T^{2} - 10178224 T + 19260741458944 \)
T^2 - 10178224*T + 19260741458944
$83$
\( T^{2} + 7214100 T + 13004909778816 \)
T^2 + 7214100*T + 13004909778816
$89$
\( T^{2} + 15330828 T + 49903967496996 \)
T^2 + 15330828*T + 49903967496996
$97$
\( T^{2} - 14024020 T + 49147910866084 \)
T^2 - 14024020*T + 49147910866084
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