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Properties

Label 1323.4.bm
Level $1323$
Weight $4$
Character orbit 1323.bm
Rep. character $\chi_{1323}(64,\cdot)$
Character field $\Q(\zeta_{21})$
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.bm (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{21})\)
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

\( 1992 q + 5 q^{2} + 651 q^{4} - 15 q^{5} + 52 q^{8} + O(q^{10}) \) \( 1992 q + 5 q^{2} + 651 q^{4} - 15 q^{5} + 52 q^{8} - 52 q^{10} + 5 q^{11} - 29 q^{13} - 172 q^{14} + 2571 q^{16} + 196 q^{17} + 72 q^{19} + 5 q^{20} - 37 q^{22} - 205 q^{23} + 3945 q^{25} + 836 q^{26} - 360 q^{28} + 215 q^{29} + 108 q^{31} + 889 q^{32} + 11 q^{34} - 526 q^{35} - 860 q^{37} + 169 q^{38} + 341 q^{40} - 583 q^{41} - 173 q^{43} - 1232 q^{44} - 2572 q^{46} - 1265 q^{47} - 324 q^{49} + 18 q^{50} + 715 q^{52} + 4276 q^{53} + 2540 q^{55} - 2887 q^{56} - 1297 q^{58} - 911 q^{59} - 2069 q^{61} + 2220 q^{62} - 19764 q^{64} + 1289 q^{65} + 576 q^{67} + 8906 q^{68} + 311 q^{70} - 5720 q^{71} - 692 q^{73} - 459 q^{74} - 1317 q^{76} + 788 q^{77} - 684 q^{79} - 35536 q^{80} - 52 q^{82} - 3067 q^{83} + 245 q^{85} + 4713 q^{86} + 779 q^{88} - 5476 q^{89} + 1030 q^{91} + 8239 q^{92} + 1187 q^{94} - 994 q^{95} - 540 q^{97} + 22044 q^{98} + O(q^{100}) \)

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

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