[N,k,chi] = [20,18,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, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("20.1");
S:= CuspForms(chi, 18);
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 \(\beta = 18\sqrt{247521}\).
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
\( T_{3}^{2} - 10980T_{3} - 50056704 \)
T3^2 - 10980*T3 - 50056704
acting on \(S_{18}^{\mathrm{new}}(\Gamma_0(20))\).
$p$
$F_p(T)$
$2$
\( T^{2} \)
T^2
$3$
\( T^{2} - 10980 T - 50056704 \)
T^2 - 10980*T - 50056704
$5$
\( (T - 390625)^{2} \)
(T - 390625)^2
$7$
\( T^{2} + 10044860 T - 1846510250144 \)
T^2 + 10044860*T - 1846510250144
$11$
\( T^{2} + 956727120 T - 40\!\cdots\!00 \)
T^2 + 956727120*T - 403412969093662800
$13$
\( T^{2} + 1231480820 T - 17\!\cdots\!44 \)
T^2 + 1231480820*T - 1781942449613526044
$17$
\( T^{2} + 27288798060 T - 12\!\cdots\!96 \)
T^2 + 27288798060*T - 1251181108104008562396
$19$
\( T^{2} + 35527896968 T + 31\!\cdots\!56 \)
T^2 + 35527896968*T + 313311066916667720656
$23$
\( T^{2} - 314831989980 T - 21\!\cdots\!36 \)
T^2 - 314831989980*T - 217142004357846987464736
$29$
\( T^{2} - 491350241052 T - 92\!\cdots\!24 \)
T^2 - 491350241052*T - 9245505798298886091953724
$31$
\( T^{2} + 3840010967528 T + 35\!\cdots\!96 \)
T^2 + 3840010967528*T + 3534396774748185227197696
$37$
\( T^{2} + 28379654425940 T + 17\!\cdots\!76 \)
T^2 + 28379654425940*T + 171718997171461266392213476
$41$
\( T^{2} + 71857168552668 T + 11\!\cdots\!56 \)
T^2 + 71857168552668*T + 1199969774570197801046481156
$43$
\( T^{2} + 84474258771260 T + 14\!\cdots\!00 \)
T^2 + 84474258771260*T + 1406604696539101945196874400
$47$
\( T^{2} + 268222754609100 T + 12\!\cdots\!44 \)
T^2 + 268222754609100*T + 12112759689646542374618823744
$53$
\( T^{2} + 407783381107140 T + 17\!\cdots\!24 \)
T^2 + 407783381107140*T + 17273302718305287411001958724
$59$
\( T^{2} + \cdots + 51\!\cdots\!44 \)
T^2 + 1468770829559976*T + 515431865070855057348277977744
$61$
\( T^{2} - 167375322642364 T - 57\!\cdots\!76 \)
T^2 - 167375322642364*T - 573361602450485481845972676476
$67$
\( T^{2} + \cdots - 19\!\cdots\!84 \)
T^2 - 5755588923766060*T - 1932688200454263450072055292384
$71$
\( T^{2} + \cdots - 68\!\cdots\!56 \)
T^2 + 2346325475416824*T - 68361508306030775797355223545856
$73$
\( T^{2} + \cdots + 39\!\cdots\!76 \)
T^2 - 12742204777546180*T + 39729358814861018019444295908676
$79$
\( T^{2} + \cdots - 25\!\cdots\!96 \)
T^2 - 13823582395154896*T - 25445540936354003158672821149696
$83$
\( T^{2} + \cdots + 11\!\cdots\!84 \)
T^2 - 10669587622913700*T + 11181850497158298574922211720384
$89$
\( T^{2} + \cdots - 18\!\cdots\!64 \)
T^2 - 26577073216629588*T - 1882681028119948147062508211803164
$97$
\( T^{2} + \cdots + 10\!\cdots\!36 \)
T^2 + 64801639405599020*T + 1005369370603078973091648458416036
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