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Properties

Label 1323.2.cf
Level $1323$
Weight $2$
Character orbit 1323.cf
Rep. character $\chi_{1323}(47,\cdot)$
Character field $\Q(\zeta_{126})$
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.cf (of order \(126\) and degree \(36\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1323 \)
Character field: \(\Q(\zeta_{126})\)
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

\( 5976 q - 39 q^{2} - 33 q^{3} - 39 q^{4} - 33 q^{5} + 24 q^{6} - 36 q^{7} - 45 q^{8} - 39 q^{9} + O(q^{10}) \) \( 5976 q - 39 q^{2} - 33 q^{3} - 39 q^{4} - 33 q^{5} + 24 q^{6} - 36 q^{7} - 45 q^{8} - 39 q^{9} - 12 q^{10} - 39 q^{11} - 33 q^{12} - 42 q^{13} - 210 q^{14} - 30 q^{15} - 27 q^{16} - 54 q^{17} - 18 q^{18} - 54 q^{19} - 24 q^{20} - 57 q^{21} - 30 q^{22} - 111 q^{23} - 6 q^{24} - 39 q^{25} - 42 q^{27} - 72 q^{28} - 174 q^{29} - 18 q^{30} - 54 q^{31} - 51 q^{32} - 33 q^{33} - 60 q^{34} - 54 q^{35} - 294 q^{36} - 15 q^{37} - 75 q^{38} - 9 q^{39} - 33 q^{40} - 42 q^{41} + 267 q^{42} - 30 q^{43} - 63 q^{44} + 21 q^{45} - 15 q^{46} + 39 q^{47} - 72 q^{49} - 63 q^{50} - 75 q^{51} - 33 q^{52} + 270 q^{53} - 159 q^{54} - 84 q^{55} + 9 q^{56} - 30 q^{57} - 39 q^{58} - 33 q^{59} + 33 q^{60} + 21 q^{61} - 162 q^{62} - 9 q^{63} - 471 q^{64} - 18 q^{65} - 105 q^{66} - 18 q^{67} - 207 q^{68} - 438 q^{69} - 27 q^{70} - 45 q^{71} - 51 q^{72} - 21 q^{73} - 51 q^{74} + 219 q^{75} - 90 q^{76} + 15 q^{77} - 48 q^{78} - 18 q^{79} + 72 q^{80} - 39 q^{81} - 66 q^{82} - 132 q^{83} - 324 q^{84} - 15 q^{85} - 93 q^{86} - 33 q^{87} - 87 q^{88} - 54 q^{89} + 39 q^{90} + 90 q^{92} - 219 q^{93} - 33 q^{94} - 150 q^{95} - 789 q^{96} + 117 q^{98} + O(q^{100}) \)

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.