Newform invariants
The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion .
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 subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(273, [\chi])\):
\( T_{2}^{112} - 242 T_{2}^{108} + 33605 T_{2}^{104} - 3152030 T_{2}^{100} + 221630758 T_{2}^{96} - 12146123884 T_{2}^{92} + 535268243529 T_{2}^{88} - 19244548977438 T_{2}^{84} + \cdots + 42\!\cdots\!41 \)
T2^112 - 242*T2^108 + 33605*T2^104 - 3152030*T2^100 + 221630758*T2^96 - 12146123884*T2^92 + 535268243529*T2^88 - 19244548977438*T2^84 + 571531364156364*T2^80 - 14087419199051836*T2^76 + 289371402969369848*T2^72 - 4947544815600179222*T2^68 + 70325135619674275312*T2^64 - 825891083362765260718*T2^60 + 7972128152964277438287*T2^56 - 62534656970261644424566*T2^52 + 395373865993299788105839*T2^48 - 1976538819243115954313132*T2^44 + 7714878230752995812498137*T2^40 - 22668136225995317214192338*T2^36 + 49480223013185711954874138*T2^32 - 72944950171055391523562452*T2^28 + 68431162019210861568858530*T2^24 - 18939997212760164158126778*T2^20 + 3766090228782095742127941*T2^16 - 365135200078911904684368*T2^12 + 25205300558855823695534*T2^8 - 106070068600492137124*T2^4 + 421301638652745841
\( T_{5}^{112} - 882 T_{5}^{108} + 456457 T_{5}^{104} - 157971354 T_{5}^{100} + 40834781064 T_{5}^{96} - 8078915475000 T_{5}^{92} + \cdots + 27\!\cdots\!76 \)
T5^112 - 882*T5^108 + 456457*T5^104 - 157971354*T5^100 + 40834781064*T5^96 - 8078915475000*T5^92 + 1262487309973485*T5^88 - 156189528458475184*T5^84 + 15465815506348258083*T5^80 - 1214839847978749680632*T5^76 + 75653861075346976192461*T5^72 - 3645804993148278500727088*T5^68 + 134499721421576454676980201*T5^64 - 3592822498821587566062713838*T5^60 + 68636649603551965699235079246*T5^56 - 812830903838947194267037274706*T5^52 + 6926247291760602252170316988006*T5^48 - 41064835212451037482734516707676*T5^44 + 180142781840508447944564146539396*T5^40 - 542833553794273143048880012433348*T5^36 + 1169523632706045629273775828776161*T5^32 - 1499377974262428251194370832021680*T5^28 + 1371787011209022459881661626139424*T5^24 - 752608103208928875292550654425088*T5^20 + 284480609913662017750972578155264*T5^16 - 40525316003592617935197689757696*T5^12 + 4273718558751695773703621582848*T5^8 - 343640974709329952384417792*T5^4 + 27610424190746351435776
\( T_{19}^{56} - 20 T_{19}^{55} + 200 T_{19}^{54} - 1956 T_{19}^{53} + 15541 T_{19}^{52} - 71276 T_{19}^{51} + 230288 T_{19}^{50} + 87122 T_{19}^{49} - 13087904 T_{19}^{48} + 87101224 T_{19}^{47} + \cdots + 88\!\cdots\!25 \)
T19^56 - 20*T19^55 + 200*T19^54 - 1956*T19^53 + 15541*T19^52 - 71276*T19^51 + 230288*T19^50 + 87122*T19^49 - 13087904*T19^48 + 87101224*T19^47 - 333626032*T19^46 + 614257792*T19^45 + 12192800159*T19^44 - 110068954864*T19^43 + 555768503610*T19^42 - 2734650750678*T19^41 + 4652402504145*T19^40 + 22640422699612*T19^39 - 153729637440626*T19^38 + 1065836747607532*T19^37 - 3127800855517798*T19^36 - 4910220432153312*T19^35 + 47936699927081150*T19^34 - 410959341215141580*T19^33 + 2040350933409896529*T19^32 - 4349647432786143224*T19^31 + 14513644087952283956*T19^30 - 28308976505383991184*T19^29 - 102314418941743731253*T19^28 + 69830763303226627912*T19^27 + 8744389502254459458*T19^26 + 2970126623315837821690*T19^25 + 4836637190825093663877*T19^24 - 13073894607098794005676*T19^23 - 31661651104481730287134*T19^22 - 50442116166856136274396*T19^21 - 87696424553585703426174*T19^20 + 100724292066962664043424*T19^19 + 746472094179434834779418*T19^18 + 1891144969124758835776388*T19^17 + 4054799083319981736456309*T19^16 + 7325991269713980225751968*T19^15 + 10791186901403444719770084*T19^14 + 14232534587557031083032408*T19^13 + 17035321736525587120984839*T19^12 + 17575026587861262396638448*T19^11 + 16108619748409848216692246*T19^10 + 13464377313745918712790394*T19^9 + 9540671759853458683245172*T19^8 + 5614747283113833478785512*T19^7 + 2925179734773123729764662*T19^6 + 1138817725156812837826904*T19^5 + 168867203697339052084449*T19^4 - 25609191340135807594060*T19^3 + 925657717104802976450*T19^2 - 127964895351481106750*T19 + 8845069910685750625