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.
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\( p \)
Sign
\(17\)
\(-1\)
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{10}^{\mathrm{new}}(\Gamma_0(289))\):
\( T_{2}^{26} - 32 T_{2}^{25} - 9472 T_{2}^{24} + 294912 T_{2}^{23} + 38993919 T_{2}^{22} - 1179754716 T_{2}^{21} - 91560086140 T_{2}^{20} + 2688404815616 T_{2}^{19} + \cdots - 60\!\cdots\!00 \)
T2^26 - 32*T2^25 - 9472*T2^24 + 294912*T2^23 + 38993919*T2^22 - 1179754716*T2^21 - 91560086140*T2^20 + 2688404815616*T2^19 + 135296082676992*T2^18 - 3849720228654208*T2^17 - 131007903986713344*T2^16 + 3603867142622328320*T2^15 + 84021475101232944384*T2^14 - 2222789082278651309056*T2^13 - 35371642253690302116864*T2^12 + 887592346652081765507072*T2^11 + 9563584211619025505566720*T2^10 - 219149950124571639354753024*T2^9 - 1628209961974003896397332480*T2^8 + 30660559064251214953822814208*T2^7 + 176068751980481225950786224128*T2^6 - 2067732999079058227916613615616*T2^5 - 11661098643913522862091837374464*T2^4 + 43812217553763761454775401447424*T2^3 + 305084254732557544741879198777344*T2^2 + 196034048215902394426742108323840*T2 - 603515986974327961514528682803200
\( T_{3}^{52} - 682344 T_{3}^{50} + 216870628408 T_{3}^{48} + \cdots + 32\!\cdots\!88 \)
T3^52 - 682344*T3^50 + 216870628408*T3^48 - 42690191892590400*T3^46 + 5837990981607084194160*T3^44 - 589758336087205363159439872*T3^42 + 45690076675983171302364278423360*T3^40 - 2781922751203311657891694933144899840*T3^38 + 135345655109080620265705925674005685406304*T3^36 - 5321230401454703312891373088594944926145106176*T3^34 + 170318113770625062880855124731807853639784729441792*T3^32 - 4457432417931408792278788149146343258474758106121300992*T3^30 + 95557104046889536390272584088342527111720408249826800717568*T3^28 - 1677097604225078731586151524494095914341603062514483420279762944*T3^26 + 24029075318679508175378455877488304754436648475965559913437627882496*T3^24 - 279588274170542524289549276213161398190220871068731664879162734660694016*T3^22 + 2620941893297386673042570981442966720857920337803128666615707706073772564736*T3^20 - 19576706311547330276170341908494745762913658779354663302157435105996995452618752*T3^18 + 114786582686065236207883809191992392702194735183306214063991197142282015128344340480*T3^16 - 518040844729803650476715865052512438161906653859424659989227278831016700787361516945408*T3^14 + 1753864442497931950894080597984988168235729475193567576419717105844974176933892402680070144*T3^12 - 4308785108512032085764234669022560988371372215580652660222940778815984811427348917339632173056*T3^10 + 7362195819520658293317743427267452856450890090755552985788233562374614627018815690307216432431104*T3^8 - 8288016609812272859246922147524308928986025051782293544782742061165055423068926719315699707808841728*T3^6 + 5707009471181846176088219998982877028502231264235955855409963615026614686456564594706724180808608776192*T3^4 - 2128554900896948064099292968049557300422864181450601903541220813368542954978682937661258940932724839415808*T3^2 + 324876949549552388562352700875732783866153389374372562104571235745423039265344134497175832147827485665394688