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Properties

Label 1323.4.be
Level $1323$
Weight $4$
Character orbit 1323.be
Rep. character $\chi_{1323}(68,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $2136$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1323.be (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 189 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1323, [\chi])\).

Total New Old
Modular forms 3072 2184 888
Cusp forms 2976 2136 840
Eisenstein series 96 48 48

Trace form

\( 2136 q + 3 q^{2} + 9 q^{3} + 3 q^{4} + 9 q^{5} - 36 q^{6} - 36 q^{8} + 99 q^{9} + O(q^{10}) \) \( 2136 q + 3 q^{2} + 9 q^{3} + 3 q^{4} + 9 q^{5} - 36 q^{6} - 36 q^{8} + 99 q^{9} - 21 q^{11} + 9 q^{12} - 288 q^{15} - 21 q^{16} + 18 q^{17} + 3 q^{18} - 72 q^{20} - 24 q^{22} + 441 q^{23} + 9 q^{24} + 3 q^{25} - 150 q^{29} + 903 q^{30} + 9 q^{31} + 1767 q^{32} + 9 q^{33} + 72 q^{34} + 1530 q^{36} - 3 q^{37} - 2601 q^{38} - 1995 q^{39} + 1134 q^{40} - 24 q^{43} + 9 q^{44} + 9 q^{45} - 3 q^{46} + 603 q^{47} - 2991 q^{50} - 15 q^{51} + 9 q^{52} + 1260 q^{53} + 6147 q^{54} + 1671 q^{57} + 3 q^{58} + 2259 q^{59} + 7047 q^{60} + 9 q^{61} + 1881 q^{62} + 62964 q^{64} + 6363 q^{65} + 9 q^{66} + 3 q^{67} - 7056 q^{68} + 7020 q^{69} - 756 q^{71} - 13197 q^{72} + 9 q^{73} + 12279 q^{74} - 4221 q^{75} - 576 q^{76} + 2646 q^{78} - 2805 q^{79} - 4608 q^{80} - 1125 q^{81} + 18 q^{82} + 5490 q^{83} + 4671 q^{85} - 19053 q^{86} + 1539 q^{87} + 2979 q^{88} + 18 q^{89} - 6561 q^{90} - 13452 q^{92} + 4599 q^{93} + 9 q^{94} - 7017 q^{95} + 4617 q^{96} - 1440 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1323, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1323, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1323, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)