[N,k,chi] = [24,22,Mod(1,24)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(24, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("24.1");
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
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
\( T_{5}^{3} + 4833126T_{5}^{2} - 396686171190900T_{5} + 389262902874527045000 \)
T5^3 + 4833126*T5^2 - 396686171190900*T5 + 389262902874527045000
acting on \(S_{22}^{\mathrm{new}}(\Gamma_0(24))\).
$p$
$F_p(T)$
$2$
\( T^{3} \)
T^3
$3$
\( (T + 59049)^{3} \)
(T + 59049)^3
$5$
\( T^{3} + 4833126 T^{2} + \cdots + 38\!\cdots\!00 \)
T^3 + 4833126*T^2 - 396686171190900*T + 389262902874527045000
$7$
\( T^{3} - 271431024 T^{2} + \cdots + 50\!\cdots\!00 \)
T^3 - 271431024*T^2 - 1287641777901937920*T + 502054947607972735220428800
$11$
\( T^{3} - 61194658188 T^{2} + \cdots - 90\!\cdots\!00 \)
T^3 - 61194658188*T^2 - 5960065597609626842064*T - 90346579001031472174389755713600
$13$
\( T^{3} + 594486202422 T^{2} + \cdots - 47\!\cdots\!16 \)
T^3 + 594486202422*T^2 - 778750167670271163481140*T - 479311615698148579479714010186492216
$17$
\( T^{3} - 1424819519334 T^{2} + \cdots - 16\!\cdots\!52 \)
T^3 - 1424819519334*T^2 - 107687025015367175844869748*T - 164168581399701320719156049397726582152
$19$
\( T^{3} + 35094825681804 T^{2} + \cdots - 23\!\cdots\!64 \)
T^3 + 35094825681804*T^2 - 960175283512356547968574416*T - 23983059364198323288993329251718873008064
$23$
\( T^{3} + 94911043073592 T^{2} + \cdots - 20\!\cdots\!88 \)
T^3 + 94911043073592*T^2 - 122021218019319898194672185664*T - 20073073766861238684066124246676005649356288
$29$
\( T^{3} + \cdots - 34\!\cdots\!24 \)
T^3 + 3292734981070734*T^2 - 3969887204510738489054484918036*T - 3451539387917192314246364206838093059623835224
$31$
\( T^{3} + \cdots - 39\!\cdots\!00 \)
T^3 + 1928658139449144*T^2 - 20620583567815029352278027575616*T - 39951999835070069496943939676316138108798195200
$37$
\( T^{3} + \cdots + 74\!\cdots\!76 \)
T^3 - 22185275061682722*T^2 - 2583651709208449162935460742921172*T + 74142603012127653358325717464804091237322892051176
$41$
\( T^{3} + \cdots + 15\!\cdots\!40 \)
T^3 - 167394191883971118*T^2 + 4007850626154148873624402592249196*T + 15110649218653474263352338455251320340836946554840
$43$
\( T^{3} + \cdots - 51\!\cdots\!56 \)
T^3 - 69547615491362508*T^2 - 1537074165932128235448150086146512*T - 5139488979301466890950770428050982099472992545856
$47$
\( T^{3} + \cdots - 12\!\cdots\!00 \)
T^3 + 49110618973894752*T^2 - 97609857783065112234152249424737280*T - 12508430563984782222736366304610179338637271910809600
$53$
\( T^{3} + \cdots - 61\!\cdots\!40 \)
T^3 - 488391341947078074*T^2 - 2181463364865326911643529654986696436*T - 614119343126713779028070093615359503255225383333115640
$59$
\( T^{3} + \cdots - 34\!\cdots\!00 \)
T^3 + 1846144806145488852*T^2 - 15601381546667591041582715748791292624*T - 34753261828623448649388457798624889196542328914718798400
$61$
\( T^{3} + \cdots - 15\!\cdots\!24 \)
T^3 - 8183707455377473002*T^2 + 20944277573840033790154201769856168780*T - 15988245679067112841983447863723056828111855178408260024
$67$
\( T^{3} + \cdots + 17\!\cdots\!24 \)
T^3 - 37438935583939030164*T^2 + 280684724669717264721618694804647995184*T + 17627654593952595659196764325784004868866042817595369024
$71$
\( T^{3} + \cdots - 72\!\cdots\!00 \)
T^3 - 65865243803437791096*T^2 + 1249328080580600448595791899579636531904*T - 7272269345436783512989451367117032895962782384088189811200
$73$
\( T^{3} + \cdots + 15\!\cdots\!00 \)
T^3 - 88415465494171854846*T^2 + 1610427983348366594118226620175610137260*T + 15313808185227942204630222384849198851256839427352027803800
$79$
\( T^{3} + \cdots + 31\!\cdots\!36 \)
T^3 - 221381156829825400920*T^2 + 9423901850078809194540809329188935218368*T + 317175435732919227082888311620424961833699445532837594164736
$83$
\( T^{3} + \cdots - 57\!\cdots\!32 \)
T^3 - 305200914127129955700*T^2 + 24128008078023229149372752138747752633392*T - 570170661341532696774582520362293757938396975031346411984832
$89$
\( T^{3} + \cdots + 32\!\cdots\!88 \)
T^3 - 327556458098783035470*T^2 - 3030722432231812378104157332648474277908*T + 3204616865019292920870949847672767277843410432245155509779288
$97$
\( T^{3} + \cdots + 19\!\cdots\!32 \)
T^3 - 1980043166774365090758*T^2 + 771139445629330058128440290510582002646796*T + 192895254317008514163671368444401352721545767441378658541687032
show more
show less