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Properties

Label 1323.2.cb
Level $1323$
Weight $2$
Character orbit 1323.cb
Rep. character $\chi_{1323}(22,\cdot)$
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.cb (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

\( 5976 q - 30 q^{2} - 30 q^{3} - 30 q^{4} - 30 q^{5} - 36 q^{7} - 15 q^{8} - 30 q^{9} + O(q^{10}) \) \( 5976 q - 30 q^{2} - 30 q^{3} - 30 q^{4} - 30 q^{5} - 36 q^{7} - 15 q^{8} - 30 q^{9} - 15 q^{10} - 30 q^{11} - 30 q^{12} - 30 q^{13} + 48 q^{14} - 30 q^{15} - 42 q^{16} - 39 q^{17} - 72 q^{18} - 36 q^{19} - 42 q^{20} - 30 q^{21} - 30 q^{22} - 120 q^{23} - 78 q^{24} - 30 q^{25} + 12 q^{26} - 30 q^{27} - 72 q^{28} + 60 q^{29} - 18 q^{30} - 72 q^{31} - 54 q^{32} + 6 q^{33} - 42 q^{34} - 9 q^{35} - 15 q^{37} - 60 q^{38} - 60 q^{39} - 84 q^{40} - 6 q^{41} + 138 q^{42} - 30 q^{43} - 15 q^{44} - 66 q^{45} - 15 q^{46} - 210 q^{47} + 24 q^{48} - 54 q^{49} - 150 q^{50} - 66 q^{51} - 6 q^{52} + 90 q^{53} + 102 q^{54} - 60 q^{55} - 9 q^{56} + 60 q^{57} - 30 q^{58} - 60 q^{59} - 138 q^{60} - 66 q^{61} + 3 q^{62} - 51 q^{63} + 441 q^{64} - 72 q^{65} - 30 q^{66} - 72 q^{67} - 108 q^{68} + 144 q^{69} - 27 q^{70} - 15 q^{71} - 138 q^{72} - 33 q^{73} - 78 q^{74} + 30 q^{75} + 30 q^{76} - 57 q^{77} + 6 q^{78} - 72 q^{79} - 1248 q^{80} - 30 q^{81} - 60 q^{82} - 90 q^{83} + 207 q^{84} - 60 q^{85} - 138 q^{86} + 36 q^{87} - 90 q^{88} - 87 q^{89} - 84 q^{90} - 27 q^{91} - 414 q^{92} + 150 q^{93} + 42 q^{94} + 189 q^{95} + 192 q^{96} - 72 q^{97} - 33 q^{98} + 360 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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