↑

Properties

Label 1323.4.bl
Level $1323$
Weight $4$
Character orbit 1323.bl
Rep. character $\chi_{1323}(100,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $1992$
Sturm bound $672$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1323.bl (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

\( 1992 q + 8 q^{2} + 648 q^{4} + 45 q^{5} + 4 q^{8} + O(q^{10}) \) \( 1992 q + 8 q^{2} + 648 q^{4} + 45 q^{5} + 4 q^{8} - 10 q^{10} + 5 q^{11} + 7 q^{13} + 278 q^{14} + 2544 q^{16} - 134 q^{17} - 72 q^{19} - 355 q^{20} + 11 q^{22} - 205 q^{23} - 7905 q^{25} - 238 q^{26} + 144 q^{28} + 341 q^{29} - 54 q^{31} - 386 q^{32} - 13 q^{34} + 317 q^{35} - 1118 q^{37} + 1417 q^{38} - 43 q^{40} - 685 q^{41} + 79 q^{43} - 479 q^{44} - 3286 q^{46} - 74 q^{47} + 270 q^{49} + 9 q^{50} + 667 q^{52} - 1850 q^{53} - 1300 q^{55} + 7721 q^{56} - 1297 q^{58} - 1658 q^{59} + 5434 q^{61} + 1896 q^{62} - 19332 q^{64} - 634 q^{65} - 288 q^{67} - 20086 q^{68} + 1037 q^{70} + 2890 q^{71} + 310 q^{73} - 411 q^{74} - 1461 q^{76} - 2902 q^{77} + 342 q^{79} + 10877 q^{80} - 34 q^{82} - 1153 q^{83} - 130 q^{85} + 4713 q^{86} + 731 q^{88} + 2588 q^{89} - 1580 q^{91} + 9853 q^{92} + 1184 q^{94} + 1445 q^{95} + 252 q^{97} - 9027 q^{98} + O(q^{100}) \)

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

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