Properties

Label 1323.2.cc
Level $1323$
Weight $2$
Character orbit 1323.cc
Rep. character $\chi_{1323}(4,\cdot)$
Character field $\Q(\zeta_{63})$
Dimension $5976$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.cc (of order \(63\) and degree \(36\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1323 \)
Character field: \(\Q(\zeta_{63})\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1323, [\chi])\).

Total New Old
Modular forms 6120 6120 0
Cusp forms 5976 5976 0
Eisenstein series 144 144 0

Trace form

\( 5976 q - 39 q^{2} - 39 q^{3} - 39 q^{4} - 39 q^{5} - 108 q^{6} - 36 q^{7} - 15 q^{8} - 39 q^{9} + O(q^{10}) \) \( 5976 q - 39 q^{2} - 39 q^{3} - 39 q^{4} - 39 q^{5} - 108 q^{6} - 36 q^{7} - 15 q^{8} - 39 q^{9} - 24 q^{10} - 39 q^{11} - 39 q^{12} - 30 q^{13} - 222 q^{14} - 30 q^{15} - 51 q^{16} - 48 q^{17} - 18 q^{18} + 18 q^{19} - 24 q^{20} - 57 q^{21} - 30 q^{22} + 33 q^{23} + 30 q^{24} - 39 q^{25} - 114 q^{26} - 30 q^{27} - 72 q^{28} + 114 q^{29} - 18 q^{30} - 18 q^{31} - 27 q^{32} - 57 q^{33} - 24 q^{34} - 36 q^{35} - 234 q^{36} - 15 q^{37} - 69 q^{38} - 69 q^{39} - 93 q^{40} - 42 q^{41} - 339 q^{42} - 30 q^{43} - 15 q^{44} - 21 q^{45} - 15 q^{46} + 105 q^{47} - 174 q^{48} - 33 q^{50} - 75 q^{51} - 51 q^{52} - 198 q^{53} - 33 q^{54} - 60 q^{55} - 153 q^{56} + 114 q^{57} - 39 q^{58} - 69 q^{59} - 39 q^{60} - 21 q^{61} - 96 q^{62} - 105 q^{63} + 441 q^{64} - 18 q^{65} - 39 q^{66} - 18 q^{67} + 9 q^{68} - 540 q^{69} - 81 q^{70} - 15 q^{71} - 147 q^{72} + 21 q^{73} - 51 q^{74} - 249 q^{75} + 66 q^{76} - 57 q^{77} - 48 q^{78} - 18 q^{79} + 444 q^{80} - 39 q^{81} - 78 q^{82} + 54 q^{84} - 15 q^{85} + 15 q^{86} - 117 q^{87} + 9 q^{88} - 96 q^{89} - 3 q^{90} + 162 q^{92} + 141 q^{93} - 75 q^{94} + 72 q^{95} - 627 q^{96} - 72 q^{97} + 183 q^{98} - 288 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1323, [\chi])\) into newform subspaces

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