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Properties

Label 9.22.c
Level $9$
Weight $22$
Character orbit 9.c
Rep. character $\chi_{9}(4,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $40$
Newform subspaces $1$
Sturm bound $22$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 9 = 3^{2} \)
Weight: \( k \) \(=\) \( 22 \)
Character orbit: \([\chi]\) \(=\) 9.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
Sturm bound: \(22\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(9, [\chi])\).

Total New Old
Modular forms 44 44 0
Cusp forms 40 40 0
Eisenstein series 4 4 0

Trace form

\( 40 q + 1023 q^{2} + 128841 q^{3} - 19922945 q^{4} + 32234853 q^{5} + 187115031 q^{6} - 189623959 q^{7} - 1296271662 q^{8} + 10117230687 q^{9} + O(q^{10}) \) \( 40 q + 1023 q^{2} + 128841 q^{3} - 19922945 q^{4} + 32234853 q^{5} + 187115031 q^{6} - 189623959 q^{7} - 1296271662 q^{8} + 10117230687 q^{9} + 4194300 q^{10} + 146068576386 q^{11} - 287594221404 q^{12} - 177565977277 q^{13} + 1549677244440 q^{14} - 5069511951597 q^{15} - 18691699769345 q^{16} - 18615603749598 q^{17} + 35716321080900 q^{18} - 9768733723954 q^{19} + 76202257650204 q^{20} - 25195769607435 q^{21} + 86758343554047 q^{22} + 356460494884095 q^{23} + 410684147823429 q^{24} - 1379841857082329 q^{25} + 4509080239093464 q^{26} - 3576595918397832 q^{27} + 1599477148286972 q^{28} - 2772828270755157 q^{29} + 3993479924773464 q^{30} + 3064842508546901 q^{31} + 9763241440878495 q^{32} - 4293613576965348 q^{33} + 5532390311666553 q^{34} - 57889578635103594 q^{35} + 85851013073070195 q^{36} + 30082698487879388 q^{37} + 38173338977409867 q^{38} - 87846860189874705 q^{39} - 43546396391926176 q^{40} + 4985514195953106 q^{41} + 337199075744914674 q^{42} - 41986108659289660 q^{43} + 309819550937094042 q^{44} - 626346227021430807 q^{45} - 741003239171632200 q^{46} + 971751895603333665 q^{47} - 2063048917232418717 q^{48} - 1393736132530446381 q^{49} + 1504393427506051923 q^{50} + 2354897151685709901 q^{51} - 892509168437820382 q^{52} - 6400936694928489300 q^{53} + 99342864988461945 q^{54} + 3526658855224378230 q^{55} + 9313401575284840590 q^{56} - 13459209464247889803 q^{57} - 985520139125952432 q^{58} + 11335149505478767926 q^{59} + 51156044998564987188 q^{60} - 333769931007960067 q^{61} - 61644391774413093852 q^{62} - 13230441185793947541 q^{63} + 25609201125502545922 q^{64} + 24815104795645584999 q^{65} - 123823169645858161830 q^{66} + 14325054629523996728 q^{67} + 98193137232148637751 q^{68} + 150864702504537503655 q^{69} - 23664205955002266174 q^{70} - 217438227096249463920 q^{71} - 48892048794664809957 q^{72} - 4831088596512341626 q^{73} + 284989967381657148240 q^{74} - 257510560866332897127 q^{75} + 45502930505046158765 q^{76} + 209785238565183158133 q^{77} + 427374495269366745654 q^{78} + 45386959469213650259 q^{79} - 998031008510384761248 q^{80} - 257436670304083233285 q^{81} + 228516181628552966154 q^{82} + 224083700347690062915 q^{83} - 475322036714517671646 q^{84} - 135764416394391341394 q^{85} - 210501162447733500423 q^{86} + 656183537067073653567 q^{87} + 409557505702705259691 q^{88} + 281885809391320932720 q^{89} - 317064997814377319892 q^{90} - 387169009858825345418 q^{91} + 160981359902419031922 q^{92} + 580984338398858289255 q^{93} + 1246412695298803268064 q^{94} + 583111881346045719228 q^{95} - 4879256367050568317232 q^{96} - 658984791485125488346 q^{97} + 5342632206895563334686 q^{98} + 1652708587690791985041 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{22}^{\mathrm{new}}(9, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
9.22.c.a 9.c 9.c $40$ $25.153$ None \(1023\) \(128841\) \(32234853\) \(-189623959\) $\mathrm{SU}(2)[C_{3}]$