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Properties

Label 1323.2.bh
Level $1323$
Weight $2$
Character orbit 1323.bh
Rep. character $\chi_{1323}(362,\cdot)$
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.bh (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

\( 696 q + 3 q^{2} + 9 q^{3} + 3 q^{4} + 9 q^{5} - 18 q^{6} - 36 q^{8} + 27 q^{9} + O(q^{10}) \) \( 696 q + 3 q^{2} + 9 q^{3} + 3 q^{4} + 9 q^{5} - 18 q^{6} - 36 q^{8} + 27 q^{9} + 9 q^{10} - 21 q^{11} + 9 q^{12} + 15 q^{16} + 9 q^{17} + 3 q^{18} + 9 q^{19} + 18 q^{20} - 24 q^{22} - 54 q^{23} + 36 q^{24} + 3 q^{25} - 42 q^{29} - 51 q^{30} + 9 q^{31} + 111 q^{32} + 9 q^{33} - 18 q^{34} - 36 q^{36} + 6 q^{37} + 9 q^{38} - 15 q^{39} + 9 q^{40} - 24 q^{43} + 63 q^{45} + 6 q^{46} - 45 q^{47} - 39 q^{50} + 21 q^{51} + 9 q^{52} - 45 q^{53} - 117 q^{54} - 48 q^{57} + 3 q^{58} + 9 q^{59} - 45 q^{60} + 63 q^{61} - 99 q^{62} + 252 q^{64} + 180 q^{65} - 63 q^{66} + 3 q^{67} - 144 q^{68} + 108 q^{69} - 108 q^{71} - 21 q^{72} + 3 q^{74} + 9 q^{75} + 36 q^{76} - 162 q^{78} + 39 q^{79} + 72 q^{80} - 117 q^{81} + 18 q^{82} - 90 q^{83} - 81 q^{85} + 117 q^{86} + 9 q^{87} + 27 q^{88} + 9 q^{89} + 81 q^{90} - 258 q^{92} + 99 q^{93} + 9 q^{94} - 141 q^{95} + 9 q^{96} - 144 q^{99} + O(q^{100}) \)

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

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