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Properties

Label 1339.2.k
Level $1339$
Weight $2$
Character orbit 1339.k
Rep. character $\chi_{1339}(355,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $238$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1339 = 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1339.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1339 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(242\)

Dimensions

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

Total New Old
Modular forms 246 246 0
Cusp forms 238 238 0
Eisenstein series 8 8 0

Trace form

\( 238 q - 5 q^{3} - 234 q^{4} - 3 q^{6} - 112 q^{9} + O(q^{10}) \) \( 238 q - 5 q^{3} - 234 q^{4} - 3 q^{6} - 112 q^{9} + 4 q^{10} + 5 q^{12} - 4 q^{13} - 12 q^{15} + 206 q^{16} - 4 q^{17} - 3 q^{18} + 24 q^{19} - 27 q^{20} - 3 q^{21} - 12 q^{22} - 4 q^{23} - 30 q^{24} + 109 q^{25} + 16 q^{26} + 28 q^{27} - 6 q^{29} + 21 q^{30} - 3 q^{35} + 90 q^{36} + 9 q^{37} + q^{39} - 8 q^{40} - 10 q^{42} + 26 q^{43} - 48 q^{44} - 6 q^{46} + 6 q^{47} - 56 q^{48} - 200 q^{49} - 3 q^{50} + 45 q^{51} + 54 q^{52} - 9 q^{53} - 24 q^{55} - 40 q^{56} - 12 q^{57} + 12 q^{59} + 66 q^{60} + 5 q^{61} - 10 q^{62} - 15 q^{63} - 152 q^{64} + 28 q^{65} + 20 q^{66} + 54 q^{67} + 76 q^{68} + 45 q^{69} + 36 q^{70} + 87 q^{72} + 29 q^{74} - 92 q^{75} - 120 q^{76} + 17 q^{77} - 17 q^{78} + 44 q^{79} + 81 q^{80} - 99 q^{81} - 12 q^{82} - 15 q^{83} + 27 q^{84} - 3 q^{85} + 42 q^{86} - 57 q^{87} + 74 q^{88} - 42 q^{89} + 20 q^{90} + 55 q^{91} - 36 q^{92} - 9 q^{93} + 36 q^{94} + 7 q^{95} + 171 q^{96} - 75 q^{99} + O(q^{100}) \)

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.