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Properties

Label 1323.2.ca
Level $1323$
Weight $2$
Character orbit 1323.ca
Rep. character $\chi_{1323}(25,\cdot)$
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.ca (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

\( 5976 q - 39 q^{2} - 39 q^{3} - 39 q^{4} - 39 q^{5} + 18 q^{6} - 36 q^{7} - 15 q^{8} - 39 q^{9} + O(q^{10}) \) \( 5976 q - 39 q^{2} - 39 q^{3} - 39 q^{4} - 39 q^{5} + 18 q^{6} - 36 q^{7} - 15 q^{8} - 39 q^{9} - 15 q^{10} - 39 q^{11} - 39 q^{12} - 30 q^{13} + 48 q^{14} - 30 q^{15} - 33 q^{16} + 33 q^{17} - 18 q^{18} - 36 q^{19} - 24 q^{20} - 21 q^{21} - 30 q^{22} + 33 q^{23} - 87 q^{24} - 39 q^{25} - 114 q^{26} - 30 q^{27} - 72 q^{28} - 264 q^{29} + 36 q^{30} - 18 q^{31} - 63 q^{32} - 57 q^{33} - 24 q^{34} - 9 q^{35} + 144 q^{36} - 24 q^{37} - 69 q^{38} - 24 q^{39} + 24 q^{40} - 42 q^{41} + 93 q^{42} - 30 q^{43} - 24 q^{44} - 75 q^{45} - 24 q^{46} + 105 q^{47} - 174 q^{48} - 54 q^{49} - 33 q^{50} + 6 q^{51} - 51 q^{52} - 198 q^{53} + 21 q^{54} - 60 q^{55} - 99 q^{56} - 264 q^{57} - 39 q^{58} - 24 q^{59} - 93 q^{60} - 75 q^{61} - 96 q^{62} - 105 q^{63} + 441 q^{64} - 81 q^{65} - 111 q^{66} - 18 q^{67} - 27 q^{68} + 216 q^{69} - 15 q^{71} + 15 q^{72} - 42 q^{73} - 33 q^{74} + 66 q^{75} - 186 q^{76} - 129 q^{77} - 48 q^{78} - 18 q^{79} + 444 q^{80} - 39 q^{81} - 78 q^{82} + 225 q^{84} - 15 q^{85} - 147 q^{86} - 72 q^{87} - 99 q^{88} + 129 q^{89} - 3 q^{90} - 27 q^{91} + 162 q^{92} + 249 q^{93} - 75 q^{94} - 153 q^{95} + 255 q^{96} - 72 q^{97} - 204 q^{98} - 288 q^{99} + O(q^{100}) \)

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.