[N,k,chi] = [5,24,Mod(1,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 24, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.1");
S:= CuspForms(chi, 24);
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
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{4} + 780T_{2}^{3} - 22815912T_{2}^{2} + 16729054720T_{2} + 38396524609536 \)
T2^4 + 780*T2^3 - 22815912*T2^2 + 16729054720*T2 + 38396524609536
acting on \(S_{24}^{\mathrm{new}}(\Gamma_0(5))\).
$p$
$F_p(T)$
$2$
\( T^{4} + 780 T^{3} + \cdots + 38396524609536 \)
T^4 + 780*T^3 - 22815912*T^2 + 16729054720*T + 38396524609536
$3$
\( T^{4} + 206680 T^{3} + \cdots + 24\!\cdots\!56 \)
T^4 + 206680*T^3 - 284909721768*T^2 - 51214770878332320*T + 2413248613110603395856
$5$
\( (T + 48828125)^{4} \)
(T + 48828125)^4
$7$
\( T^{4} + 1010710600 T^{3} + \cdots + 47\!\cdots\!96 \)
T^4 + 1010710600*T^3 - 68102977629902330472*T^2 - 138839300648872394086420581600*T + 47660145324072641036945823347957895696
$11$
\( T^{4} - 510770963328 T^{3} + \cdots + 37\!\cdots\!76 \)
T^4 - 510770963328*T^3 - 1827478697311561501126656*T^2 + 43343826615221238871267744471318528*T + 370947859421241500580538084442838260896996786176
$13$
\( T^{4} + 14153856943960 T^{3} + \cdots - 12\!\cdots\!84 \)
T^4 + 14153856943960*T^3 - 3879804831784804988413608*T^2 - 559222369747111962346328790301022004640*T - 1283951140660311242853456178277573162234698640671984
$17$
\( T^{4} - 15332090016360 T^{3} + \cdots + 20\!\cdots\!16 \)
T^4 - 15332090016360*T^3 - 30022434303840797498894308392*T^2 + 280965119206038005800972611905414467704160*T + 200032149501417988556595327241055150028449856434685036816
$19$
\( T^{4} + \cdots + 93\!\cdots\!00 \)
T^4 - 1111809672255440*T^3 + 194007647121307850802443330400*T^2 + 48632240096233840993504359659593902128864000*T + 939819757052908286809157743026385082576817600531082400000
$23$
\( T^{4} + \cdots - 25\!\cdots\!24 \)
T^4 + 3998020505342040*T^3 - 68442411483674278669945506363048*T^2 - 303052935691965344204733938473350527604185657760*T - 258680257593500042641523683216445527532567974989098434737091824
$29$
\( T^{4} + \cdots - 13\!\cdots\!00 \)
T^4 + 170274795551093640*T^3 + 4866579307647353150147782288133400*T^2 - 356819828289661449954568747762055452583832664684000*T - 13517985808977958319743730146139932991271925228349364648673704150000
$31$
\( T^{4} + \cdots + 14\!\cdots\!96 \)
T^4 + 172942006080462832*T^3 - 2672794763686436882369318475712416*T^2 - 926105023688916972625852797969510081489014304260352*T + 14258926530094577724477222779622559882254307717681741280787708477696
$37$
\( T^{4} + \cdots + 14\!\cdots\!56 \)
T^4 - 461695977491285480*T^3 - 381687732794493069549077175427918632*T^2 + 43315170895100603891679627820458267654927304457354080*T + 14298047226676718617075563455240015724841741580537965381564907947357456
$41$
\( T^{4} + \cdots - 13\!\cdots\!44 \)
T^4 - 1746066900841990488*T^3 - 17056178963468672130986310066195030696*T^2 + 34121767561090946477658619745988701210364948156527496608*T - 13853073012465956768100043628965383493483228102928536774641499137295586544
$43$
\( T^{4} + \cdots + 14\!\cdots\!96 \)
T^4 - 13231308551430609800*T^3 + 39417161059755148327651254463150050072*T^2 - 19146525051363941053864158371632275192650916437401952800*T + 1415041781551428762390916975253797508797178940369444599156376874920801296
$47$
\( T^{4} + \cdots - 13\!\cdots\!24 \)
T^4 + 25463181064945728360*T^3 + 106419026441963408502736390438992345048*T^2 - 578928347793377138585917463867677569739445984207358865760*T - 1306473432205223431566051588389558855994640125540266206936165831968505911024
$53$
\( T^{4} + \cdots + 23\!\cdots\!56 \)
T^4 - 19153511824499883720*T^3 - 10420272056932539218480761697544679723368*T^2 + 386738117732375059040305858001070719855608392498213763053280*T + 2390450627428015240920023411718285503338815281323567421354602702197754409930256
$59$
\( T^{4} + \cdots + 16\!\cdots\!00 \)
T^4 - 217218038347313160720*T^3 - 82724486274778307357244442086144135530400*T^2 + 6774724024695375168040718628076532868747039562293197162848000*T + 1636576581179909842876124726184827701100430224317122234822922146199512234928800000
$61$
\( T^{4} + \cdots + 61\!\cdots\!76 \)
T^4 - 152379678911827122728*T^3 - 167719351333642567629701937925522509689256*T^2 + 13321296655378790494561554460567858286778092788166737842501728*T + 6110136330038412885939118136416892836041319285112963194683189412134967198624495376
$67$
\( T^{4} + \cdots - 10\!\cdots\!84 \)
T^4 + 2317407910895557756840*T^3 - 121087106790777720891732349184167964173992*T^2 - 2692082386266625034849908524170102490819849351022466409569939040*T - 1085140201260024753712384730442570625129542450482930846688153755966446121327338681584
$71$
\( T^{4} + \cdots + 94\!\cdots\!36 \)
T^4 - 1453247054528140867248*T^3 - 3132821279493216829962140565579041715339936*T^2 + 2762629229338899262891467936360520096368515786583062095494802688*T + 949686861659328167587893090551533954317104504545369336504013787450226434506089902336
$73$
\( T^{4} + \cdots - 10\!\cdots\!24 \)
T^4 - 2601821824581282121160*T^3 - 9289253072009877683217490002082529407539048*T^2 + 26833283960569374522791104790626856305944930457116096392461411040*T - 10010021861983419973324515839883554808667882767520984695670372447669302968897206499824
$79$
\( T^{4} + \cdots + 33\!\cdots\!00 \)
T^4 - 22817266427547282683360*T^3 + 167055100513125588959415247224264027316310400*T^2 - 433322097534193164743285246663835732516241481176972268001540864000*T + 339537099424832418708744500686501419649675900834087352732015274683827106478535027200000
$83$
\( T^{4} + \cdots + 14\!\cdots\!36 \)
T^4 - 49081293110242175251080*T^3 + 842212269628644669759618025597488477902431512*T^2 - 5903073393579736721870235464040312500425501322024864707185087067680*T + 14427895815267510111089275189623725611614037591953230502716961245386358149666075587537936
$89$
\( T^{4} + \cdots - 15\!\cdots\!00 \)
T^4 - 50023669870473477290280*T^3 - 737479439059805431526609083224250435021631400*T^2 + 43313694681479150967009781598256648505983604579732377552019355772000*T - 156993042208075199503716478953726413568650347779083945956904336979213196384511421372150000
$97$
\( T^{4} + \cdots - 35\!\cdots\!24 \)
T^4 + 141223261544238546490360*T^3 - 10106631204170137486440410359584580109385701352*T^2 - 1792693885988489369108710394358030680222305929410791959672629675593760*T - 35218347034620635712857539575892252072488280488583957765993959306549853272052858640314736624
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