Characteristic polynomials of the Hecke operator T2 on Gamma0(7) for weights up to 36

Level 7, Rational newforms page

{4, 1 + x}

{6, (10 + x)*(6 - 9*x + x^2)}

{8, (6 + x)*(-214 + 3*x + x^2)}

{10, (-184 + 6*x + x^2)*(19080 - 1326*x - 21*x^2 + x^3)}

{12, (-2640 + 54*x + x^2)*(225104 - 2854*x - 77*x^2 + x^3)}

{14, (590720 - 20776*x - 26*x^2 + x^3)* (4351104 - 806760*x - 15294*x^2 + 27*x^3 + x^4)}

{16, (-4450176 + 18816*x + 438*x^2 + x^3)* (555779200 + 2911584*x - 97142*x^2 - 93*x^3 + x^4)}

{18, (10531932160 + 27034368*x - 236696*x^2 - 186*x^3 + x^4)* (-1167515043840 - 8750693376*x + 253624680*x^2 - 416814*x^3 - 597*x^4 + x^5)}

{20, (207467274240 - 467202816*x - 1278192*x^2 + 342*x^3 + x^4)*(119291562532864 + 861102886144*x - 129845456*x^2 - 2198822*x^3 + 115*x^4 + x^5)}

{22, (21247798784819200 + 8182869766144*x - 17655966080*x^2 - 7583624*x^3 + 2278*x^4 + x^5)* (-2046860254016962560 - 10159131488514048*x + 3162211853184*x^2 + 15611869368*x^3 - 5971038*x^4 - 2565*x^5 + x^6)}

{24, (42669499801927680 + 126440549720064*x + 443260800*x^2 - 27993696*x^3 + 1014*x^4 + x^5)* (-72994235208910766080 - 5303389957300224*x + 143562378079104*x^2 - 30209992704*x^3 - 26133462*x^4 + 2115*x^5 + x^6)}

{26, (4242135922016874659840 + 9273501511959969792*x + 4144865943312384*x^2 - 374552082432*x^3 - 135046008*x^4 + 4230*x^5 + x^6)*(742372109292552973776322560 - 161929219207629001457664*x - 56891995107349469184*x^2 + 10057437525973248*x^3 + 1307318457096*x^4 - 182203278*x^5 - 8373*x^6 + x^7)}

{28, (-528268602034224019537920 + 72034091088046718976*x + 26399887398273024*x^2 - 2146228752384*x^3 - 407865552*x^4 + 7830*x^5 + x^6)*(23819583599774856090925137920 - 6656199810331026677825536*x - 902635897846727442432*x^2 + 119597861752332288*x^3 + 7776265405392*x^4 - 619118982*x^5 - 16109*x^6 + x^7)}

{30, (715115211611902508288442368000 - 429136393421133606383779840*x - 8902969223929918390272*x^2 + 2711314145733033984*x^3 + 3072852162432*x^4 - 3274369128*x^5 + 550*x^6 + x^7)* (7413330781887320911926516976189440 - 331303215879680724916374601728*x - 947979595577992040429912064*x^2 + 15718398838853606866944*x^3 + 3318976580980028544*x^4 - 21310916973480*x^5 - 3319431102*x^6 + 8091*x^7 + x^8)}

{32, (-106271390445043801180362705469440 + 17238391562536929142530637824*x + 1201245041536516969463808*x^2 - 8224392295266435072*x^3 - 919156905468288*x^4 - 5636277312*x^5 + 114486*x^6 + x^7)*(-2090008956704800874070756612752015360 + 503905133805841784527493630263296*x - 10062867624956320024172167168*x^2 - 1018779004587746329214976*x^3 + 26466410576733809280*x^4 + 392591098887840*x^5 - 10188132406*x^6 - 41757*x^7 + x^8)}

{34, (174840447567420360235423782965126103040 - 24398668009202616287719395371778048*x - 2707673949392043491622381420544*x^2 - 13572847816100522956947456*x^3 + 584242931322022078464*x^4 + 2397968066315520*x^5 - 42394873432*x^6 - 83514*x^7 + x^8)* (-292909192103434788636943418456508762528153600 + 14907555990652791090168547356632458199040*x + 344002226777658021722573380226383872*x^2 - 6249236713885547641888628539392*x^3 - 71783427754621648353650688*x^4 + 925775568575913162240*x^5 + 4884478608940200*x^6 - 53165475054*x^7 - 103701*x^8 + x^9)}

{36, (-14746877113236991706093542186483187712000 - 4489358660449485929422395472682680320*x - 178258565121743036393050211352576*x^2 + 824281541011056844380045312*x^3 + 9345889013349467824128*x^4 - 24143739772015872*x^5 - 167936936112*x^6 + 185814*x^7 + x^8)* (-414464814037228878275560194956425705936859955200 + 6918526510304970692469601693116895483396096*x + 38486771020246010287860312210900254720*x^2 - 748852721086259291867040053198848*x^3 - 1320085247130874827374665728*x^4 + 24281131375431346907904*x^5 + 13892831855073392*x^6 - 275002417126*x^7 - 46157*x^8 + x^9)}