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Properties

Label 1323.4.x
Level $1323$
Weight $4$
Character orbit 1323.x
Rep. character $\chi_{1323}(214,\cdot)$
Character field $\Q(\zeta_{9})$
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.x (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 189 \)
Character field: \(\Q(\zeta_{9})\)
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

\( 2136 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 12 q^{8} + 99 q^{9} + O(q^{10}) \) \( 2136 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 12 q^{8} + 99 q^{9} + 6 q^{10} + 27 q^{11} + 3 q^{12} + 12 q^{13} + 240 q^{15} + 27 q^{16} - 810 q^{17} + 3 q^{18} + 6 q^{19} + 36 q^{20} - 24 q^{22} - 435 q^{23} - 909 q^{24} + 3 q^{25} + 942 q^{26} + 12 q^{27} + 102 q^{29} - 897 q^{30} + 3 q^{31} + 999 q^{32} - 285 q^{33} + 36 q^{34} - 570 q^{36} - 3 q^{37} - 771 q^{38} - 2415 q^{39} + 1146 q^{40} - 1224 q^{41} - 24 q^{43} - 3 q^{44} - 1977 q^{45} - 3 q^{46} - 195 q^{47} + 234 q^{48} - 2241 q^{50} - 15 q^{51} - 45 q^{52} - 414 q^{53} - 2043 q^{54} + 24 q^{55} + 1833 q^{57} + 3 q^{58} - 747 q^{59} + 1023 q^{60} - 105 q^{61} + 2355 q^{62} - 62988 q^{64} + 2523 q^{65} - 717 q^{66} + 3 q^{67} + 5430 q^{68} - 3972 q^{69} + 228 q^{71} - 8973 q^{72} + 429 q^{73} - 9561 q^{74} - 2943 q^{75} + 204 q^{76} - 11562 q^{78} + 2811 q^{79} + 5190 q^{80} - 3861 q^{81} + 6 q^{82} + 1842 q^{83} - 3969 q^{85} + 2379 q^{86} + 2337 q^{87} - 2973 q^{88} - 12810 q^{89} + 2199 q^{90} - 2508 q^{92} - 4593 q^{93} - 3669 q^{94} - 9489 q^{95} + 6615 q^{96} + 12 q^{97} + 6432 q^{99} + O(q^{100}) \)

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

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