[N,k,chi] = [18,42,Mod(1,18)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(18, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 42, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("18.1");
S:= CuspForms(chi, 42);
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
\( T_{5} - 48504195130650 \)
T5 - 48504195130650
acting on \(S_{42}^{\mathrm{new}}(\Gamma_0(18))\).
$p$
$F_p(T)$
$2$
\( T - 1048576 \)
T - 1048576
$3$
\( T \)
T
$5$
\( T - 48504195130650 \)
T - 48504195130650
$7$
\( T + 11\!\cdots\!68 \)
T + 119392445696650168
$11$
\( T + 31\!\cdots\!52 \)
T + 3153808852281809358252
$13$
\( T + 11\!\cdots\!74 \)
T + 11410299686425943429074
$17$
\( T - 26\!\cdots\!58 \)
T - 26723760622401267203746158
$19$
\( T - 67\!\cdots\!60 \)
T - 67975218671585815673353460
$23$
\( T - 13\!\cdots\!04 \)
T - 13505073711965391061204062504
$29$
\( T + 13\!\cdots\!10 \)
T + 136715473782261984486517330110
$31$
\( T - 30\!\cdots\!12 \)
T - 3061422960031285210493644903712
$37$
\( T + 22\!\cdots\!78 \)
T + 221949310451710778755633026909178
$41$
\( T - 50\!\cdots\!38 \)
T - 501985001900072034529449934630038
$43$
\( T + 31\!\cdots\!84 \)
T + 3118478207799237814439067265458484
$47$
\( T + 13\!\cdots\!92 \)
T + 13155518377394721101101992302953392
$53$
\( T - 32\!\cdots\!14 \)
T - 323998598696161709213951685217879914
$59$
\( T + 34\!\cdots\!20 \)
T + 3459574233993702447512816107676048220
$61$
\( T + 97\!\cdots\!78 \)
T + 978043389864200648530692366749996578
$67$
\( T - 16\!\cdots\!52 \)
T - 16627547762843789524411885842685183652
$71$
\( T + 11\!\cdots\!32 \)
T + 116968857862178710569082285660379434632
$73$
\( T - 19\!\cdots\!66 \)
T - 190708537939407193015711554853622755466
$79$
\( T + 56\!\cdots\!80 \)
T + 561362454250092673715323867778422642480
$83$
\( T - 60\!\cdots\!84 \)
T - 605770926784301808468900622973886535884
$89$
\( T + 11\!\cdots\!90 \)
T + 11915426835300121180468989518247227755290
$97$
\( T + 63\!\cdots\!98 \)
T + 63576010574535484047856854187104758743198
show more
show less