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Properties

Label 9.44
Level 9
Weight 44
Dimension 102
Nonzero newspaces 2
Newform subspaces 5
Sturm bound 264
Trace bound 1

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Defining parameters

Level: \( N \) = \( 9 = 3^{2} \)
Weight: \( k \) = \( 44 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 5 \)
Sturm bound: \(264\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{44}(\Gamma_1(9))\).

Total New Old
Modular forms 133 107 26
Cusp forms 125 102 23
Eisenstein series 8 5 3

Trace form

\( 102 q - 6404247 q^{2} - 13941084612 q^{3} - 93369333357645 q^{4} - 2001960217825200 q^{5} + 162206321154798663 q^{6} + 1592391163760904228 q^{7} - 47822758637833021302 q^{8} + 146271049366174834122 q^{9} + O(q^{10}) \) \( 102 q - 6404247 q^{2} - 13941084612 q^{3} - 93369333357645 q^{4} - 2001960217825200 q^{5} + 162206321154798663 q^{6} + 1592391163760904228 q^{7} - 47822758637833021302 q^{8} + 146271049366174834122 q^{9} - 5537154985343965902528 q^{10} - 34883616812299044737904 q^{11} - 740568675095560042787820 q^{12} - 987015684765331522638588 q^{13} + 4442284289078481668638608 q^{14} - 4808475576569476903009068 q^{15} - 270350508943353824854453617 q^{16} + 1789277411513982010340589192 q^{17} + 2574952739521858830613028796 q^{18} - 2128609787513013617377588752 q^{19} - 12961344793598964028397414988 q^{20} + 104107490035438421145052909776 q^{21} + 160304229161508855753167138631 q^{22} - 157876173880420494771068726988 q^{23} - 1615844320672205119006735420995 q^{24} - 4824069714507731395765094636604 q^{25} - 17208606813849126959090968685772 q^{26} + 20661242108008294433387919102768 q^{27} + 67808276489475170305103196176892 q^{28} - 64250743808932410078943125672492 q^{29} - 24088727913493100913745994207232 q^{30} + 442620103828495395242499444857724 q^{31} - 688484723330048115353321808706257 q^{32} + 297048719614299665351279285606382 q^{33} + 2804093507477049635651588893798389 q^{34} + 11246610958850333702682051968969496 q^{35} - 9964224060479024649298451823103245 q^{36} - 5443050533575089015067586337184692 q^{37} + 14229414407603194421302103229410787 q^{38} + 22878533587080777440425307223345084 q^{39} - 102248779585040372235801939527928744 q^{40} + 37881033423381949010343579107589618 q^{41} + 772559756044092151556902267703904882 q^{42} + 52558005859993444759196226975470040 q^{43} + 1958353820903475733049311582972852650 q^{44} - 1749103198861950331352840086805139660 q^{45} + 334380199003198126165251058013571816 q^{46} - 3710600097852791421312160929889153356 q^{47} + 1776134119660035141031711565017808355 q^{48} + 994201710295942491703521220312785900 q^{49} - 1524086123533736983315149846930149871 q^{50} + 6477911078617460914878028514944550076 q^{51} - 31101156478081743466162252557589698846 q^{52} + 945479428822641966239601070370965332 q^{53} + 42387784655483889297192938597963210745 q^{54} + 14399739314280765743559415700477023224 q^{55} + 100349372664833623264876844071074111534 q^{56} + 85428197726684607692536027693429872714 q^{57} + 17080684237403698599280131533558282916 q^{58} - 124902503599736076439898341477250092224 q^{59} + 205214403405035252104614466050399091884 q^{60} + 66834476568579359636064588928630720992 q^{61} + 1970893192008561991796527083032821284708 q^{62} - 2261509067065945323367351645919779975452 q^{63} + 10272663842973765224861475681235274776962 q^{64} - 3741217688951505111706261261467673649580 q^{65} + 2608718859148058319417836821833708579690 q^{66} + 2381673738325953065824261934057765957280 q^{67} - 14706860902798391775659088285463935292905 q^{68} + 21936511928762355736504753672845769927596 q^{69} - 35815892029104010979817551571253904318238 q^{70} + 69843550524625913965515110873443486150656 q^{71} - 82473174357701448799327928013798575237973 q^{72} + 27483429656570193298546572712877315394936 q^{73} - 23216258320504345719540719848662449287068 q^{74} - 71022532581450781225207960684487252895588 q^{75} - 19912647777866367653273833576811756548227 q^{76} + 6407019835725025864560810596031567647640 q^{77} - 70075067517342900061323985338297826877226 q^{78} + 101081489455728826637853985860081677018244 q^{79} - 1008373483243588023277779772713423585663648 q^{80} + 377597792008383733485838057721851466714538 q^{81} + 479997084866950093701649108479139870312518 q^{82} + 119109204517202455024407823347635570019852 q^{83} + 23312028186555494425944234564202272983226 q^{84} - 3633313194281015858910716789063768076024 q^{85} + 596980346198781295213560216368634355890273 q^{86} - 617164507110530067473617976751246147837564 q^{87} + 1762967687055914665408031972006193800533899 q^{88} - 1775961339887538603857155793648329951461180 q^{89} - 1833133750341414021117660968952255519909876 q^{90} + 2568698935120563864376945672883387825907240 q^{91} + 2784809645850907539654412862578163586874146 q^{92} - 4742084473197819713916314081612006270250564 q^{93} + 14564784237066984847024342829797542000361080 q^{94} - 20477635624605502290328257331643189923773648 q^{95} - 21805600332058229271858445896883322160579048 q^{96} + 11910526514068548841607480313935120491925178 q^{97} - 38478989000961007459679890658771716844949336 q^{98} + 14863033715208923677821973930891664171627508 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{44}^{\mathrm{new}}(\Gamma_1(9))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
9.44.a \(\chi_{9}(1, \cdot)\) 9.44.a.a 3 1
9.44.a.b 3
9.44.a.c 4
9.44.a.d 8
9.44.c \(\chi_{9}(4, \cdot)\) 9.44.c.a 84 2

Decomposition of \(S_{44}^{\mathrm{old}}(\Gamma_1(9))\) into lower level spaces

\( S_{44}^{\mathrm{old}}(\Gamma_1(9)) \cong \) \(S_{44}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{44}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)