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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

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

Display 100 coefficients 10 coefficients

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

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