[N,k,chi] = [36,22,Mod(1,36)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(36, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("36.1");
S:= CuspForms(chi, 22);
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
\( p \)
Sign
\(2\)
\(-1\)
\(3\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5} - 11268090 \)
T5 - 11268090
acting on \(S_{22}^{\mathrm{new}}(\Gamma_0(36))\).
$p$
$F_p(T)$
$2$
\( T \)
T
$3$
\( T \)
T
$5$
\( T - 11268090 \)
T - 11268090
$7$
\( T - 281914136 \)
T - 281914136
$11$
\( T - 36172082484 \)
T - 36172082484
$13$
\( T + 449098578370 \)
T + 449098578370
$17$
\( T + 2121858786546 \)
T + 2121858786546
$19$
\( T + 4609406233900 \)
T + 4609406233900
$23$
\( T + 95095276921656 \)
T + 95095276921656
$29$
\( T - 2245742383351266 \)
T - 2245742383351266
$31$
\( T + 3155693201792656 \)
T + 3155693201792656
$37$
\( T + 18\!\cdots\!82 \)
T + 18178503074861482
$41$
\( T - 16\!\cdots\!10 \)
T - 169649739387485910
$43$
\( T + 15\!\cdots\!44 \)
T + 158968551608988244
$47$
\( T - 13\!\cdots\!36 \)
T - 134697468442682736
$53$
\( T - 15\!\cdots\!38 \)
T - 15637375269722538
$59$
\( T + 29\!\cdots\!84 \)
T + 2977241337691499484
$61$
\( T - 36\!\cdots\!02 \)
T - 3603855625679330702
$67$
\( T - 21\!\cdots\!04 \)
T - 21066199531967164004
$71$
\( T + 21\!\cdots\!60 \)
T + 21980089544074358760
$73$
\( T + 17\!\cdots\!22 \)
T + 17054415965500339222
$79$
\( T + 11\!\cdots\!52 \)
T + 115020124425041803552
$83$
\( T - 96\!\cdots\!44 \)
T - 96628520442403345644
$89$
\( T + 60\!\cdots\!50 \)
T + 60427571095732966650
$97$
\( T + 40\!\cdots\!98 \)
T + 407820224794143352798
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