Properties

Label 1323.2.cc
Level $1323$
Weight $2$
Character orbit 1323.cc
Rep. character $\chi_{1323}(4,\cdot)$
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.cc (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

\( 5976q - 39q^{2} - 39q^{3} - 39q^{4} - 39q^{5} - 108q^{6} - 36q^{7} - 15q^{8} - 39q^{9} + O(q^{10}) \) \( 5976q - 39q^{2} - 39q^{3} - 39q^{4} - 39q^{5} - 108q^{6} - 36q^{7} - 15q^{8} - 39q^{9} - 24q^{10} - 39q^{11} - 39q^{12} - 30q^{13} - 222q^{14} - 30q^{15} - 51q^{16} - 48q^{17} - 18q^{18} + 18q^{19} - 24q^{20} - 57q^{21} - 30q^{22} + 33q^{23} + 30q^{24} - 39q^{25} - 114q^{26} - 30q^{27} - 72q^{28} + 114q^{29} - 18q^{30} - 18q^{31} - 27q^{32} - 57q^{33} - 24q^{34} - 36q^{35} - 234q^{36} - 15q^{37} - 69q^{38} - 69q^{39} - 93q^{40} - 42q^{41} - 339q^{42} - 30q^{43} - 15q^{44} - 21q^{45} - 15q^{46} + 105q^{47} - 174q^{48} - 33q^{50} - 75q^{51} - 51q^{52} - 198q^{53} - 33q^{54} - 60q^{55} - 153q^{56} + 114q^{57} - 39q^{58} - 69q^{59} - 39q^{60} - 21q^{61} - 96q^{62} - 105q^{63} + 441q^{64} - 18q^{65} - 39q^{66} - 18q^{67} + 9q^{68} - 540q^{69} - 81q^{70} - 15q^{71} - 147q^{72} + 21q^{73} - 51q^{74} - 249q^{75} + 66q^{76} - 57q^{77} - 48q^{78} - 18q^{79} + 444q^{80} - 39q^{81} - 78q^{82} + 54q^{84} - 15q^{85} + 15q^{86} - 117q^{87} + 9q^{88} - 96q^{89} - 3q^{90} + 162q^{92} + 141q^{93} - 75q^{94} + 72q^{95} - 627q^{96} - 72q^{97} + 183q^{98} - 288q^{99} + O(q^{100}) \)

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

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