Properties

Label 1323.4.cc
Level $1323$
Weight $4$
Character orbit 1323.cc
Rep. character $\chi_{1323}(4,\cdot)$
Character field $\Q(\zeta_{63})$
Dimension $18072$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1323.cc (of order \(63\) and degree \(36\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1323 \)
Character field: \(\Q(\zeta_{63})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 18216 18216 0
Cusp forms 18072 18072 0
Eisenstein series 144 144 0

Trace form

\( 18072 q - 39 q^{2} - 39 q^{3} - 39 q^{4} - 39 q^{5} + 126 q^{6} - 36 q^{7} - 15 q^{8} - 39 q^{9} + O(q^{10}) \) \( 18072 q - 39 q^{2} - 39 q^{3} - 39 q^{4} - 39 q^{5} + 126 q^{6} - 36 q^{7} - 15 q^{8} - 39 q^{9} - 24 q^{10} - 39 q^{11} - 39 q^{12} - 30 q^{13} + 732 q^{14} - 30 q^{15} - 87 q^{16} + 384 q^{17} - 18 q^{18} + 18 q^{19} - 6 q^{20} - 12 q^{21} - 30 q^{22} - 1047 q^{23} + 1542 q^{24} - 39 q^{25} + 858 q^{26} - 30 q^{27} - 72 q^{28} + 978 q^{29} - 432 q^{30} - 18 q^{31} + 153 q^{32} - 327 q^{33} - 6 q^{34} - 846 q^{35} - 7632 q^{36} - 15 q^{37} + 1821 q^{38} + 381 q^{39} - 1173 q^{40} - 1266 q^{41} + 9723 q^{42} - 30 q^{43} - 15 q^{44} + 951 q^{45} - 15 q^{46} - 1623 q^{47} + 150 q^{48} - 1224 q^{49} - 33 q^{50} - 1461 q^{51} - 87 q^{52} - 3438 q^{53} - 2625 q^{54} - 60 q^{55} - 99 q^{56} + 8682 q^{57} - 39 q^{58} + 1461 q^{59} - 3351 q^{60} + 15 q^{61} + 2334 q^{62} + 570 q^{63} + 93681 q^{64} - 1215 q^{65} - 4359 q^{66} - 18 q^{67} + 801 q^{68} + 28746 q^{69} - 1629 q^{70} - 15 q^{71} - 4791 q^{72} - 879 q^{73} - 2463 q^{74} - 24639 q^{75} + 1506 q^{76} + 4956 q^{77} - 192 q^{78} - 18 q^{79} - 41892 q^{80} - 39 q^{81} - 78 q^{82} + 1800 q^{83} + 22932 q^{84} + 345 q^{85} - 4197 q^{86} + 765 q^{87} + 1593 q^{88} + 6384 q^{89} + 2157 q^{90} + 522 q^{91} + 17928 q^{92} - 13899 q^{93} - 3711 q^{94} + 3600 q^{95} + 22269 q^{96} - 72 q^{97} + 31557 q^{98} + 16560 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1323, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.