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Properties

Label 1323.2.be
Level $1323$
Weight $2$
Character orbit 1323.be
Rep. character $\chi_{1323}(68,\cdot)$
Character field $\Q(\zeta_{18})$
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.be (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 189 \)
Character field: \(\Q(\zeta_{18})\)
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

\( 696 q + 3 q^{2} + 9 q^{3} + 3 q^{4} + 9 q^{5} + 18 q^{6} - 36 q^{8} - 9 q^{9} + O(q^{10}) \) \( 696 q + 3 q^{2} + 9 q^{3} + 3 q^{4} + 9 q^{5} + 18 q^{6} - 36 q^{8} - 9 q^{9} + 15 q^{11} + 9 q^{12} - 3 q^{16} + 18 q^{17} + 3 q^{18} - 18 q^{20} - 24 q^{22} + 18 q^{23} + 9 q^{24} + 3 q^{25} - 42 q^{29} + 57 q^{30} + 9 q^{31} - 33 q^{32} + 9 q^{33} + 18 q^{34} - 36 q^{36} - 3 q^{37} + 99 q^{38} + 84 q^{39} + 54 q^{40} - 24 q^{43} + 9 q^{44} + 9 q^{45} - 3 q^{46} - 45 q^{47} - 39 q^{50} - 60 q^{51} + 9 q^{52} + 45 q^{53} - 171 q^{54} - 48 q^{57} + 3 q^{58} - 36 q^{59} - 27 q^{60} + 9 q^{61} + 99 q^{62} + 252 q^{64} - 99 q^{65} + 9 q^{66} + 3 q^{67} - 36 q^{68} - 108 q^{69} - 108 q^{71} + 249 q^{72} + 9 q^{73} - 123 q^{74} - 36 q^{75} - 36 q^{76} - 162 q^{78} + 39 q^{79} - 72 q^{80} + 63 q^{81} + 18 q^{82} + 90 q^{83} - 81 q^{85} + 99 q^{86} + 54 q^{87} + 27 q^{88} + 18 q^{89} - 81 q^{90} - 258 q^{92} - 9 q^{93} + 9 q^{94} + 183 q^{95} + 81 q^{96} - 144 q^{99} + O(q^{100}) \)

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

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