[N,k,chi] = [80,10,Mod(1,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("80.1");
S:= CuspForms(chi, 10);
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 \(\beta = 2\sqrt{1009}\).
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
\( T_{3}^{2} + 260T_{3} + 12864 \)
T3^2 + 260*T3 + 12864
acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(80))\).
$p$
$F_p(T)$
$2$
\( T^{2} \)
T^2
$3$
\( T^{2} + 260T + 12864 \)
T^2 + 260*T + 12864
$5$
\( (T - 625)^{2} \)
(T - 625)^2
$7$
\( T^{2} + 1700 T - 45485664 \)
T^2 + 1700*T - 45485664
$11$
\( T^{2} + 23984 T - 3498681936 \)
T^2 + 23984*T - 3498681936
$13$
\( T^{2} - 115020 T + 1463044964 \)
T^2 - 115020*T + 1463044964
$17$
\( T^{2} - 412820 T - 124159138524 \)
T^2 - 412820*T - 124159138524
$19$
\( T^{2} - 296520 T + 13842837200 \)
T^2 - 296520*T + 13842837200
$23$
\( T^{2} - 1049220 T - 104453293536 \)
T^2 - 1049220*T - 104453293536
$29$
\( T^{2} + 3666980 T - 8181719994300 \)
T^2 + 3666980*T - 8181719994300
$31$
\( T^{2} + 1613144 T - 23496920418816 \)
T^2 + 1613144*T - 23496920418816
$37$
\( T^{2} + 21121940 T + 69008321696356 \)
T^2 + 21121940*T + 69008321696356
$41$
\( T^{2} + \cdots + 157181579575044 \)
T^2 + 26957276*T + 157181579575044
$43$
\( T^{2} + \cdots + 698658564887264 \)
T^2 + 52889700*T + 698658564887264
$47$
\( T^{2} + \cdots + 576652311252096 \)
T^2 + 58412180*T + 576652311252096
$53$
\( T^{2} + \cdots - 924496505573436 \)
T^2 + 39035140*T - 924496505573436
$59$
\( T^{2} - 54995560 T - 16\!\cdots\!00 \)
T^2 - 54995560*T - 1651507412377200
$61$
\( T^{2} + 274579716 T + 18\!\cdots\!64 \)
T^2 + 274579716*T + 18365331333660164
$67$
\( T^{2} - 318580 T - 58\!\cdots\!24 \)
T^2 - 318580*T - 5893006728145824
$71$
\( T^{2} - 7130936 T - 39\!\cdots\!76 \)
T^2 - 7130936*T - 39761625748190976
$73$
\( T^{2} - 120858180 T - 75\!\cdots\!36 \)
T^2 - 120858180*T - 75035909727112636
$79$
\( T^{2} + 6877520 T - 35\!\cdots\!00 \)
T^2 + 6877520*T - 355685554255948800
$83$
\( T^{2} + 1402348740 T + 48\!\cdots\!64 \)
T^2 + 1402348740*T + 484023800169310464
$89$
\( T^{2} - 830088660 T - 84\!\cdots\!00 \)
T^2 - 830088660*T - 8419187993852700
$97$
\( T^{2} - 638394580 T + 94\!\cdots\!96 \)
T^2 - 638394580*T + 94949009041932196
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