Properties

Label 1323.2.ci
Level $1323$
Weight $2$
Character orbit 1323.ci
Rep. character $\chi_{1323}(5,\cdot)$
Character field $\Q(\zeta_{126})$
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.ci (of order \(126\) and degree \(36\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1323 \)
Character field: \(\Q(\zeta_{126})\)
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

\( 5976q - 39q^{2} - 33q^{3} - 39q^{4} - 33q^{5} - 66q^{6} - 36q^{7} - 45q^{8} - 39q^{9} + O(q^{10}) \) \( 5976q - 39q^{2} - 33q^{3} - 39q^{4} - 33q^{5} - 66q^{6} - 36q^{7} - 45q^{8} - 39q^{9} - 21q^{10} - 39q^{11} - 33q^{12} - 42q^{13} + 60q^{14} - 30q^{15} - 45q^{16} - 45q^{17} - 18q^{18} - 60q^{20} - 21q^{21} - 30q^{22} - 111q^{23} - 33q^{24} - 39q^{25} - 42q^{27} - 72q^{28} + 204q^{29} - 72q^{30} - 54q^{31} - 15q^{32} - 33q^{33} - 24q^{34} - 81q^{35} + 84q^{36} - 24q^{37} + 141q^{38} - 54q^{39} + 12q^{40} - 42q^{41} - 165q^{42} - 30q^{43} - 54q^{44} - 33q^{45} - 24q^{46} + 39q^{47} - 18q^{49} - 63q^{50} + 6q^{51} - 33q^{52} - 270q^{53} - 213q^{54} - 84q^{55} - 45q^{56} - 30q^{57} - 39q^{58} - 78q^{59} - 129q^{60} - 33q^{61} + 36q^{62} - 9q^{63} - 471q^{64} - 81q^{65} - 33q^{66} - 18q^{67} - 99q^{68} + 102q^{69} - 108q^{70} - 45q^{71} - 33q^{72} - 12q^{73} - 33q^{74} - 204q^{75} + 90q^{76} - 57q^{77} - 48q^{78} - 18q^{79} - 72q^{80} - 39q^{81} - 66q^{82} + 48q^{83} - 153q^{84} - 15q^{85} + 69q^{86} + 12q^{87} + 21q^{88} - 45q^{89} - 123q^{90} - 27q^{91} + 90q^{92} - 327q^{93} - 33q^{94} + 75q^{95} + 417q^{96} + 162q^{98} + O(q^{100}) \)

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

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