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Properties

Label 1339.2.g
Level $1339$
Weight $2$
Character orbit 1339.g
Rep. character $\chi_{1339}(365,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $208$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1339 = 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1339.g (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 103 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(242\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1339, [\chi])\).

Total New Old
Modular forms 248 208 40
Cusp forms 240 208 32
Eisenstein series 8 0 8

Trace form

\( 208 q - 4 q^{3} - 104 q^{4} - 8 q^{5} + 4 q^{7} - 12 q^{8} + 196 q^{9} + O(q^{10}) \) \( 208 q - 4 q^{3} - 104 q^{4} - 8 q^{5} + 4 q^{7} - 12 q^{8} + 196 q^{9} + 32 q^{10} - 8 q^{11} - 20 q^{12} + 20 q^{14} + 2 q^{15} - 112 q^{16} - 4 q^{17} + 24 q^{18} - 4 q^{19} - 8 q^{20} - 28 q^{21} - 32 q^{22} + 4 q^{23} + 36 q^{24} - 132 q^{25} + 20 q^{27} + 12 q^{29} - 60 q^{30} + 36 q^{31} + 22 q^{32} + 18 q^{33} + 16 q^{35} - 74 q^{36} - 32 q^{37} - 12 q^{38} + 16 q^{39} - 22 q^{40} - 12 q^{41} + 12 q^{42} - 6 q^{44} + 10 q^{45} + 24 q^{46} - 60 q^{47} - 12 q^{48} - 72 q^{49} - 22 q^{50} - 36 q^{51} - 8 q^{52} + 28 q^{53} - 2 q^{54} - 8 q^{55} - 6 q^{56} - 14 q^{57} + 14 q^{58} - 2 q^{59} + 18 q^{60} + 48 q^{61} + 4 q^{62} + 46 q^{63} + 228 q^{64} - 8 q^{65} - 60 q^{66} - 40 q^{67} - 56 q^{69} - 72 q^{70} - 10 q^{71} - 156 q^{72} - 60 q^{73} - 30 q^{74} - 44 q^{75} - 28 q^{76} + 10 q^{77} + 6 q^{78} + 64 q^{80} + 80 q^{81} + 14 q^{82} - 38 q^{83} - 58 q^{84} + 18 q^{85} + 12 q^{86} - 14 q^{87} + 82 q^{88} + 144 q^{89} + 284 q^{90} - 38 q^{92} - 144 q^{93} + 144 q^{94} - 28 q^{95} - 2 q^{96} + 46 q^{97} + 22 q^{98} - 20 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1339, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1339, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1339, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(103, [\chi])\)\(^{\oplus 2}\)