Properties

Label 1323.2.cb
Level $1323$
Weight $2$
Character orbit 1323.cb
Rep. character $\chi_{1323}(22,\cdot)$
Character field $\Q(\zeta_{63})$
Dimension $5976$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.cb (of order \(63\) and degree \(36\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1323 \)
Character field: \(\Q(\zeta_{63})\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1323, [\chi])\).

Total New Old
Modular forms 6120 6120 0
Cusp forms 5976 5976 0
Eisenstein series 144 144 0

Trace form

\( 5976q - 30q^{2} - 30q^{3} - 30q^{4} - 30q^{5} - 36q^{7} - 15q^{8} - 30q^{9} + O(q^{10}) \) \( 5976q - 30q^{2} - 30q^{3} - 30q^{4} - 30q^{5} - 36q^{7} - 15q^{8} - 30q^{9} - 15q^{10} - 30q^{11} - 30q^{12} - 30q^{13} + 48q^{14} - 30q^{15} - 42q^{16} - 39q^{17} - 72q^{18} - 36q^{19} - 42q^{20} - 30q^{21} - 30q^{22} - 120q^{23} - 78q^{24} - 30q^{25} + 12q^{26} - 30q^{27} - 72q^{28} + 60q^{29} - 18q^{30} - 72q^{31} - 54q^{32} + 6q^{33} - 42q^{34} - 9q^{35} - 15q^{37} - 60q^{38} - 60q^{39} - 84q^{40} - 6q^{41} + 138q^{42} - 30q^{43} - 15q^{44} - 66q^{45} - 15q^{46} - 210q^{47} + 24q^{48} - 54q^{49} - 150q^{50} - 66q^{51} - 6q^{52} + 90q^{53} + 102q^{54} - 60q^{55} - 9q^{56} + 60q^{57} - 30q^{58} - 60q^{59} - 138q^{60} - 66q^{61} + 3q^{62} - 51q^{63} + 441q^{64} - 72q^{65} - 30q^{66} - 72q^{67} - 108q^{68} + 144q^{69} - 27q^{70} - 15q^{71} - 138q^{72} - 33q^{73} - 78q^{74} + 30q^{75} + 30q^{76} - 57q^{77} + 6q^{78} - 72q^{79} - 1248q^{80} - 30q^{81} - 60q^{82} - 90q^{83} + 207q^{84} - 60q^{85} - 138q^{86} + 36q^{87} - 90q^{88} - 87q^{89} - 84q^{90} - 27q^{91} - 414q^{92} + 150q^{93} + 42q^{94} + 189q^{95} + 192q^{96} - 72q^{97} - 33q^{98} + 360q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1323, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.