Properties

Label 1323.2.v
Level $1323$
Weight $2$
Character orbit 1323.v
Rep. character $\chi_{1323}(67,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $696$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.v (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 189 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 1056 744 312
Cusp forms 960 696 264
Eisenstein series 96 48 48

Trace form

\( 696q + 3q^{2} + 3q^{3} + 3q^{4} + 3q^{5} + 18q^{6} - 12q^{8} + 27q^{9} + O(q^{10}) \) \( 696q + 3q^{2} + 3q^{3} + 3q^{4} + 3q^{5} + 18q^{6} - 12q^{8} + 27q^{9} - 3q^{10} + 27q^{11} + 3q^{12} + 12q^{13} - 48q^{15} - 9q^{16} - 27q^{17} + 3q^{18} - 3q^{19} + 18q^{20} - 24q^{22} + 60q^{23} + 72q^{24} + 3q^{25} - 30q^{26} + 12q^{27} - 6q^{29} + 57q^{30} + 3q^{31} + 135q^{32} - 15q^{33} + 18q^{34} + 24q^{36} + 6q^{37} - 69q^{38} - 75q^{39} - 51q^{40} - 24q^{43} + 6q^{44} + 21q^{45} + 6q^{46} + 21q^{47} - 90q^{48} - 9q^{50} + 21q^{51} - 9q^{52} - 9q^{53} + 9q^{54} + 24q^{55} - 30q^{57} + 3q^{58} - 27q^{59} + 123q^{60} + 21q^{61} - 75q^{62} - 276q^{64} + 156q^{65} + 3q^{66} + 3q^{67} + 30q^{68} + 6q^{69} + 12q^{71} - 261q^{72} + 42q^{73} - 165q^{74} + 45q^{75} + 24q^{76} + 30q^{78} - 33q^{79} - 102q^{80} + 171q^{81} + 6q^{82} + 42q^{83} + 63q^{85} + 129q^{86} - 75q^{87} - 21q^{88} - 75q^{89} + 39q^{90} + 102q^{92} - 93q^{93} - 33q^{94} + 51q^{95} + 171q^{96} + 12q^{97} - 48q^{99} + O(q^{100}) \)

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

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

Decomposition of \(S_{2}^{\mathrm{old}}(1323, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1323, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)