[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 4);
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
\(43\)
\(1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{10} + T_{2}^{9} - 59 T_{2}^{8} - 42 T_{2}^{7} + 1187 T_{2}^{6} + 541 T_{2}^{5} - 9389 T_{2}^{4} - 2180 T_{2}^{3} + 22676 T_{2}^{2} + 320 T_{2} - 768 \)
T2^10 + T2^9 - 59*T2^8 - 42*T2^7 + 1187*T2^6 + 541*T2^5 - 9389*T2^4 - 2180*T2^3 + 22676*T2^2 + 320*T2 - 768
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1849))\).
$p$
$F_p(T)$
$2$
\( T^{10} + T^{9} - 59 T^{8} - 42 T^{7} + \cdots - 768 \)
T^10 + T^9 - 59*T^8 - 42*T^7 + 1187*T^6 + 541*T^5 - 9389*T^4 - 2180*T^3 + 22676*T^2 + 320*T - 768
$3$
\( T^{10} - 5 T^{9} - 181 T^{8} + \cdots - 897652 \)
T^10 - 5*T^9 - 181*T^8 + 889*T^7 + 10846*T^6 - 50844*T^5 - 232303*T^4 + 964607*T^3 + 1056433*T^2 - 2054479*T - 897652
$5$
\( T^{10} - 19 T^{9} - 520 T^{8} + \cdots + 13252064 \)
T^10 - 19*T^9 - 520*T^8 + 9730*T^7 + 81965*T^6 - 1416691*T^5 - 4536302*T^4 + 58611028*T^3 - 6619256*T^2 - 188529264*T + 13252064
$7$
\( T^{10} - 51 T^{9} + \cdots - 557226765054 \)
T^10 - 51*T^9 - 472*T^8 + 59154*T^7 - 460864*T^6 - 19675828*T^5 + 309402918*T^4 + 909505950*T^3 - 42711550225*T^2 + 276205364535*T - 557226765054
$11$
\( T^{10} - 27 T^{9} + \cdots + 54\!\cdots\!84 \)
T^10 - 27*T^9 - 8233*T^8 + 261449*T^7 + 22988393*T^6 - 876326789*T^5 - 23022732000*T^4 + 1188704099468*T^3 + 1147656418160*T^2 - 526991459558400*T + 5492460824899584
$13$
\( T^{10} - 15 T^{9} + \cdots - 16347624948144 \)
T^10 - 15*T^9 - 5909*T^8 + 133833*T^7 + 5735766*T^6 - 198314734*T^5 + 28836023*T^4 + 69699070245*T^3 - 1098413162217*T^2 + 6955317662895*T - 16347624948144
$17$
\( T^{10} - 82 T^{9} + \cdots - 55\!\cdots\!09 \)
T^10 - 82*T^9 - 17588*T^8 + 896068*T^7 + 100521763*T^6 - 3155382772*T^5 - 227244321407*T^4 + 4282912614148*T^3 + 195426352110528*T^2 - 1865173837252866*T - 55085055924133809
$19$
\( T^{10} + 78 T^{9} + \cdots + 19\!\cdots\!12 \)
T^10 + 78*T^9 - 32199*T^8 - 2574112*T^7 + 241880243*T^6 + 21425103826*T^5 - 23595142289*T^4 - 20402521951504*T^3 - 70387136687084*T^2 + 1328105939206480*T + 1941047371116112
$23$
\( T^{10} - 61 T^{9} + \cdots - 50\!\cdots\!16 \)
T^10 - 61*T^9 - 36125*T^8 + 943995*T^7 + 433272864*T^6 + 494227058*T^5 - 1771146225115*T^4 - 21831916801367*T^3 + 2463525330520003*T^2 + 41320146754005495*T - 509897708397778716
$29$
\( T^{10} - 53 T^{9} + \cdots - 99\!\cdots\!08 \)
T^10 - 53*T^9 - 102752*T^8 + 3609944*T^7 + 3005344122*T^6 - 91425123882*T^5 - 26184194262360*T^4 + 376778416650912*T^3 + 53150024805319485*T^2 - 886730409589665177*T - 9947073517241246208
$31$
\( T^{10} + 253 T^{9} + \cdots - 52\!\cdots\!08 \)
T^10 + 253*T^9 - 192026*T^8 - 50822420*T^7 + 12173369483*T^6 + 3274094305687*T^5 - 338397738535154*T^4 - 80732625233674848*T^3 + 5737216202760867328*T^2 + 721560178206497753088*T - 52823269474774092177408
$37$
\( T^{10} - 129 T^{9} + \cdots - 13\!\cdots\!22 \)
T^10 - 129*T^9 - 220911*T^8 + 18700587*T^7 + 15490797632*T^6 - 569128063150*T^5 - 398082766059421*T^4 - 2181295377095097*T^3 + 2149004004358988841*T^2 - 449284592036191203*T - 1319171512482355951422
$41$
\( T^{10} - 391 T^{9} + \cdots + 15\!\cdots\!04 \)
T^10 - 391*T^9 - 222352*T^8 + 83217062*T^7 + 16642715745*T^6 - 5392924208523*T^5 - 565574714840522*T^4 + 128032560276581100*T^3 + 6716508856304885176*T^2 - 905920240529029731264*T + 15973870482130935067904
$43$
\( T^{10} \)
T^10
$47$
\( T^{10} + 334 T^{9} + \cdots - 43\!\cdots\!36 \)
T^10 + 334*T^9 - 569197*T^8 - 186405384*T^7 + 84992121871*T^6 + 25990538762594*T^5 - 2450275820282632*T^4 - 464441904503201408*T^3 + 28080733212805344512*T^2 - 368783363001587810304*T - 432608258097735745536
$53$
\( T^{10} + 773 T^{9} + \cdots + 90\!\cdots\!28 \)
T^10 + 773*T^9 - 349537*T^8 - 315479835*T^7 + 25029246810*T^6 + 36747896129186*T^5 + 1354873925972291*T^4 - 1282383398828115091*T^3 - 84018187466013257169*T^2 + 13380168829071118241767*T + 905255909948998097072628
$59$
\( T^{10} + 1483 T^{9} + \cdots + 24\!\cdots\!52 \)
T^10 + 1483*T^9 - 675633*T^8 - 1772062747*T^7 - 101773161761*T^6 + 746926733772619*T^5 + 155132496203546580*T^4 - 133749273399512227072*T^3 - 35497323165290789983488*T^2 + 8664847000546895463185664*T + 2457358237670084844165245952
$61$
\( T^{10} + 437 T^{9} + \cdots - 87\!\cdots\!08 \)
T^10 + 437*T^9 - 1333925*T^8 - 475761867*T^7 + 657979058742*T^6 + 162064811381222*T^5 - 145610151167970093*T^4 - 15395391890023539975*T^3 + 12714148644959067308751*T^2 - 670641732751587122266153*T - 87220256147908433603105108
$67$
\( T^{10} - 642 T^{9} + \cdots + 32\!\cdots\!47 \)
T^10 - 642*T^9 - 940244*T^8 + 398545246*T^7 + 210254894129*T^6 - 79312888930826*T^5 - 10939393271534163*T^4 + 5193638878310637042*T^3 - 367549237530254301642*T^2 - 3978648412526674102356*T + 329120232511697353837647
$71$
\( T^{10} - 1545 T^{9} + \cdots - 57\!\cdots\!72 \)
T^10 - 1545*T^9 - 1027473*T^8 + 2593863625*T^7 - 504090332386*T^6 - 878877016772996*T^5 + 342409367379458413*T^4 + 37389388134073150283*T^3 - 14516395209774331354899*T^2 - 1947939169820986919726839*T - 57683327351232171359479672
$73$
\( T^{10} + 1292 T^{9} + \cdots + 12\!\cdots\!97 \)
T^10 + 1292*T^9 - 1420146*T^8 - 1983467630*T^7 + 723611840081*T^6 + 1065545103597184*T^5 - 154614818246717635*T^4 - 230085438444583197350*T^3 + 8936964441525012357654*T^2 + 15780581932872605285613960*T + 1267540695521957756662107597
$79$
\( T^{10} - 1405 T^{9} + \cdots - 28\!\cdots\!04 \)
T^10 - 1405*T^9 - 806097*T^8 + 1778738217*T^7 - 370117015666*T^6 - 381949959036740*T^5 + 194939336682703785*T^4 - 26659610404844986901*T^3 - 1086583521304465200403*T^2 + 498463203759073000458221*T - 28607672735724394166921204
$83$
\( T^{10} + 543 T^{9} + \cdots + 29\!\cdots\!08 \)
T^10 + 543*T^9 - 2212049*T^8 - 767646131*T^7 + 1490357691678*T^6 + 190060339630992*T^5 - 328182885341722743*T^4 + 43530856322857980083*T^3 + 5460988319483299029945*T^2 - 1041703304503103078573415*T + 29919976443668919924704808
$89$
\( T^{10} - 2196 T^{9} + \cdots + 31\!\cdots\!37 \)
T^10 - 2196*T^9 + 51982*T^8 + 2763317314*T^7 - 1343149444591*T^6 - 928397290434592*T^5 + 679595905770123305*T^4 + 44459615702136432714*T^3 - 76494334301634643528050*T^2 + 3709224548829780363826632*T + 316171284529407505110548937
$97$
\( T^{10} + 425 T^{9} + \cdots - 51\!\cdots\!44 \)
T^10 + 425*T^9 - 4271630*T^8 - 816237440*T^7 + 6119006283904*T^6 + 314542841159488*T^5 - 3398013476571217344*T^4 + 36555023532870085824*T^3 + 603737972603933420231552*T^2 + 6836256776894394545024000*T - 5186605075385713590075551744
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