[N,k,chi] = [2,34,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 34, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 34);
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
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
\( T_{3} + 133005564 \)
T3 + 133005564
acting on \(S_{34}^{\mathrm{new}}(\Gamma_0(2))\).
$p$
$F_p(T)$
$2$
\( T + 65536 \)
T + 65536
$3$
\( T + 133005564 \)
T + 133005564
$5$
\( T - 538799132550 \)
T - 538799132550
$7$
\( T + 33347311051768 \)
T + 33347311051768
$11$
\( T + 85\!\cdots\!28 \)
T + 85882263625386228
$13$
\( T - 11\!\cdots\!66 \)
T - 1144054008875905166
$17$
\( T + 13\!\cdots\!98 \)
T + 139113675669385621998
$19$
\( T - 80\!\cdots\!60 \)
T - 80695000174130231060
$23$
\( T + 14\!\cdots\!44 \)
T + 14120372378143910765544
$29$
\( T + 16\!\cdots\!90 \)
T + 1632686905195131326709090
$31$
\( T + 18\!\cdots\!28 \)
T + 1894078958241443951861728
$37$
\( T + 96\!\cdots\!98 \)
T + 96444218751358368990635098
$41$
\( T - 64\!\cdots\!42 \)
T - 641768233498553833164038442
$43$
\( T + 81\!\cdots\!84 \)
T + 817975597351211427387164884
$47$
\( T + 62\!\cdots\!68 \)
T + 6229246687280441243201826768
$53$
\( T + 21\!\cdots\!94 \)
T + 21322120079333214208388446794
$59$
\( T - 29\!\cdots\!20 \)
T - 298987905886407341741567881020
$61$
\( T + 45\!\cdots\!58 \)
T + 455881915835062287556960014658
$67$
\( T - 11\!\cdots\!12 \)
T - 1172332419477563429554964377412
$71$
\( T - 25\!\cdots\!72 \)
T - 2591524145775150288511661030472
$73$
\( T + 28\!\cdots\!74 \)
T + 2825174388069163226217247688374
$79$
\( T - 92\!\cdots\!20 \)
T - 920688453939087595198198640720
$83$
\( T + 16\!\cdots\!04 \)
T + 16199219945453134166417678661804
$89$
\( T + 20\!\cdots\!10 \)
T + 203491630107372946965013220025510
$97$
\( T - 22\!\cdots\!42 \)
T - 226806680667600950875216250271842
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