Properties

Label 1323.2.x
Level $1323$
Weight $2$
Character orbit 1323.x
Rep. character $\chi_{1323}(214,\cdot)$
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.x (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

\( 696q + 3q^{2} + 3q^{3} + 3q^{4} + 3q^{5} + 18q^{6} - 12q^{8} - 9q^{9} + O(q^{10}) \) \( 696q + 3q^{2} + 3q^{3} + 3q^{4} + 3q^{5} + 18q^{6} - 12q^{8} - 9q^{9} + 6q^{10} - 9q^{11} + 3q^{12} + 12q^{13} - 48q^{15} + 9q^{16} + 54q^{17} + 3q^{18} + 6q^{19} + 18q^{20} - 24q^{22} - 12q^{23} - 45q^{24} + 3q^{25} - 30q^{26} + 12q^{27} - 6q^{29} - 51q^{30} + 3q^{31} - 81q^{32} - 15q^{33} + 18q^{34} + 24q^{36} - 3q^{37} + 57q^{38} + 114q^{39} + 66q^{40} - 24q^{43} - 3q^{44} - 33q^{45} - 3q^{46} + 21q^{47} - 90q^{48} - 9q^{50} - 60q^{51} - 9q^{52} - 9q^{53} + 63q^{54} + 24q^{55} - 30q^{57} + 3q^{58} + 18q^{59} - 111q^{60} - 33q^{61} - 75q^{62} - 276q^{64} - 123q^{65} - 69q^{66} + 3q^{67} - 6q^{68} + 6q^{69} + 12q^{71} + 153q^{72} - 21q^{73} + 213q^{74} - 18q^{75} + 24q^{76} + 30q^{78} - 33q^{79} - 102q^{80} - 81q^{81} + 6q^{82} + 42q^{83} + 63q^{85} - 213q^{86} - 30q^{87} - 21q^{88} + 150q^{89} + 39q^{90} + 102q^{92} + 15q^{93} - 33q^{94} + 15q^{95} - 81q^{96} + 12q^{97} - 48q^{99} + O(q^{100}) \)

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

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