[N,k,chi] = [38,10,Mod(1,38)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(38, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("38.1");
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
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
\(2\)
\(1\)
\(19\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{4} - 84T_{3}^{3} - 44107T_{3}^{2} - 1329018T_{3} + 62650008 \)
T3^4 - 84*T3^3 - 44107*T3^2 - 1329018*T3 + 62650008
acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(38))\).
$p$
$F_p(T)$
$2$
\( (T + 16)^{4} \)
(T + 16)^4
$3$
\( T^{4} - 84 T^{3} - 44107 T^{2} + \cdots + 62650008 \)
T^4 - 84*T^3 - 44107*T^2 - 1329018*T + 62650008
$5$
\( T^{4} + 1395 T^{3} + \cdots + 15389064288000 \)
T^4 + 1395*T^3 - 7813530*T^2 - 6547343400*T + 15389064288000
$7$
\( T^{4} + \cdots + 359494671206216 \)
T^4 - 12307*T^3 - 14461281*T^2 + 244743771643*T + 359494671206216
$11$
\( T^{4} + 104249 T^{3} + \cdots + 11\!\cdots\!24 \)
T^4 + 104249*T^3 + 3398840664*T^2 + 36343268701740*T + 115765319454159024
$13$
\( T^{4} - 120486 T^{3} + \cdots + 23\!\cdots\!00 \)
T^4 - 120486*T^3 - 30806569293*T^2 + 2295095998230370*T + 239482312188112867800
$17$
\( T^{4} + 412139 T^{3} + \cdots + 27\!\cdots\!62 \)
T^4 + 412139*T^3 - 374372926323*T^2 - 99501926037315363*T + 27353310191565709750362
$19$
\( (T - 130321)^{4} \)
(T - 130321)^4
$23$
\( T^{4} - 3010300 T^{3} + \cdots + 22\!\cdots\!08 \)
T^4 - 3010300*T^3 + 862408556595*T^2 + 2126564557696334952*T + 228996364751452995758208
$29$
\( T^{4} - 6153240 T^{3} + \cdots - 34\!\cdots\!76 \)
T^4 - 6153240*T^3 + 8624111888511*T^2 + 2981737641494670876*T - 3465735658175265676349076
$31$
\( T^{4} - 12774024 T^{3} + \cdots - 14\!\cdots\!96 \)
T^4 - 12774024*T^3 + 51883371775344*T^2 - 63865994000171580800*T - 14450660213485628662173696
$37$
\( T^{4} - 20506048 T^{3} + \cdots - 58\!\cdots\!72 \)
T^4 - 20506048*T^3 - 68206760068968*T^2 + 2257729526657272857856*T - 5896773061589731421495938672
$41$
\( T^{4} - 11620300 T^{3} + \cdots - 36\!\cdots\!00 \)
T^4 - 11620300*T^3 - 531906213139500*T^2 + 6769189527301249200000*T - 369166098252924069120000000
$43$
\( T^{4} - 7698327 T^{3} + \cdots - 19\!\cdots\!12 \)
T^4 - 7698327*T^3 - 893995448146728*T^2 - 9364763321794174473296*T - 19143060939072240183264880512
$47$
\( T^{4} + 31581083 T^{3} + \cdots + 52\!\cdots\!00 \)
T^4 + 31581083*T^3 - 1669221829649832*T^2 - 19578419823909248876160*T + 526104279570536841835466956800
$53$
\( T^{4} - 72549422 T^{3} + \cdots - 20\!\cdots\!64 \)
T^4 - 72549422*T^3 - 4017930015425685*T^2 + 318019463969293786126482*T - 2021251322797490452975793768664
$59$
\( T^{4} + 149234120 T^{3} + \cdots - 27\!\cdots\!04 \)
T^4 + 149234120*T^3 + 3811888983551253*T^2 - 165305399932727330279670*T - 2797674735783276468916659428904
$61$
\( T^{4} - 129004373 T^{3} + \cdots + 43\!\cdots\!00 \)
T^4 - 129004373*T^3 - 10642541015571546*T^2 + 918155331227984210747860*T + 43184181107782200169532040064600
$67$
\( T^{4} - 132595266 T^{3} + \cdots - 18\!\cdots\!00 \)
T^4 - 132595266*T^3 - 58349865773044743*T^2 + 8416311030032755588165000*T - 180217978088559983441544591294000
$71$
\( T^{4} + 47138482 T^{3} + \cdots - 32\!\cdots\!32 \)
T^4 + 47138482*T^3 - 74119300967107956*T^2 - 10787481985125373934311944*T - 325175408613922244767130582500032
$73$
\( T^{4} + 39332795 T^{3} + \cdots + 35\!\cdots\!34 \)
T^4 + 39332795*T^3 - 87654713869556991*T^2 - 10014753479885452595184887*T + 35838529860534293009934539339834
$79$
\( T^{4} + 307010840 T^{3} + \cdots + 29\!\cdots\!00 \)
T^4 + 307010840*T^3 - 229308708527002548*T^2 + 10746082751368875164160640*T + 2916421544595378499086459663027200
$83$
\( T^{4} + 746568232 T^{3} + \cdots - 94\!\cdots\!68 \)
T^4 + 746568232*T^3 + 152802359319519228*T^2 + 2191292375220701216411904*T - 946420650629777651597145814143168
$89$
\( T^{4} - 286943482 T^{3} + \cdots + 54\!\cdots\!84 \)
T^4 - 286943482*T^3 - 451932251304917424*T^2 + 99409659763689129738797280*T + 5418152889895455270185833357411584
$97$
\( T^{4} - 793519958 T^{3} + \cdots + 37\!\cdots\!00 \)
T^4 - 793519958*T^3 - 3736940299059182196*T^2 + 1572636728151428535592075480*T + 3732769932269220506371828731733278400
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