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Properties

Label 1323.4.w
Level $1323$
Weight $4$
Character orbit 1323.w
Rep. character $\chi_{1323}(148,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $2184$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1323.w (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
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 2244 828
Cusp forms 2976 2184 792
Eisenstein series 96 60 36

Trace form

\( 2184 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 18 q^{5} + 18 q^{6} - 87 q^{8} + 54 q^{9} + O(q^{10}) \) \( 2184 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 18 q^{5} + 18 q^{6} - 87 q^{8} + 54 q^{9} + 3 q^{10} + 93 q^{11} + 159 q^{12} + 6 q^{13} + 204 q^{15} - 18 q^{16} + 207 q^{17} - 627 q^{18} + 3 q^{19} - 633 q^{20} - 84 q^{22} - 402 q^{23} + 270 q^{24} - 210 q^{25} + 66 q^{26} + 1137 q^{27} + 204 q^{29} - 213 q^{30} - 48 q^{31} + 360 q^{32} - 51 q^{33} + 252 q^{34} - 1020 q^{36} + 3 q^{37} + 180 q^{38} + 768 q^{39} - 561 q^{40} + 753 q^{41} + 483 q^{43} - 2205 q^{44} - 2328 q^{45} + 3 q^{46} + 204 q^{47} - 2031 q^{48} + 2001 q^{50} + 1731 q^{51} - 1323 q^{52} + 1080 q^{53} - 3798 q^{54} + 12 q^{55} + 1992 q^{57} - 885 q^{58} + 3750 q^{59} + 402 q^{60} - 48 q^{61} + 2118 q^{62} - 63183 q^{64} + 1302 q^{65} - 2463 q^{66} - 669 q^{67} + 183 q^{68} + 3642 q^{69} - 2877 q^{71} + 36 q^{72} + 219 q^{73} + 6591 q^{74} - 4560 q^{75} + 3054 q^{76} - 5010 q^{78} - 2802 q^{79} - 9690 q^{80} - 414 q^{81} + 12 q^{82} - 180 q^{83} - 2565 q^{85} - 1188 q^{86} - 1776 q^{87} - 114 q^{88} + 1212 q^{89} - 16872 q^{90} + 8955 q^{92} - 2598 q^{93} + 5703 q^{94} + 2583 q^{95} - 12078 q^{96} - 3369 q^{97} + 4686 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1323, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)