Properties

Label 1323.4.bz
Level $1323$
Weight $4$
Character orbit 1323.bz
Rep. character $\chi_{1323}(143,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $1992$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1323.bz (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 6120 2040 4080
Cusp forms 5976 1992 3984
Eisenstein series 144 48 96

Trace form

\( 1992 q + 21 q^{2} + 1307 q^{4} + 18 q^{5} - 12 q^{7} + O(q^{10}) \) \( 1992 q + 21 q^{2} + 1307 q^{4} + 18 q^{5} - 12 q^{7} - 22 q^{10} + 18 q^{11} + 29 q^{13} + 600 q^{14} - 5141 q^{16} - 72 q^{17} - 36 q^{19} + 45 q^{20} - 21 q^{22} - 108 q^{23} + 3942 q^{25} - 96 q^{26} + 128 q^{28} - 111 q^{29} + 21 q^{32} - 31 q^{34} + 765 q^{35} + 1066 q^{37} - 684 q^{38} - 427 q^{40} + 639 q^{41} - 89 q^{43} + 795 q^{44} + 3234 q^{46} + 1005 q^{47} + 72 q^{49} - 675 q^{50} + 2492 q^{52} + 1092 q^{53} - 2170 q^{55} + 87 q^{56} + 3252 q^{58} + 1515 q^{59} + 2933 q^{61} - 3072 q^{62} + 19548 q^{64} + 21 q^{65} + 576 q^{67} + 3525 q^{68} + 98 q^{70} + 9702 q^{71} - 22 q^{73} - 1194 q^{74} - 759 q^{76} - 4422 q^{77} - 180 q^{79} - 4239 q^{80} - 46 q^{82} + 1851 q^{83} - 130 q^{85} - 4140 q^{86} + 616 q^{88} - 10014 q^{89} + 1112 q^{91} + 6045 q^{92} - 7 q^{94} + 21 q^{95} + 792 q^{97} + 5667 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1323, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)