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Properties

Label 1339.2.h
Level $1339$
Weight $2$
Character orbit 1339.h
Rep. character $\chi_{1339}(159,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $238$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1339 = 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1339.h (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1339 \)
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 246 246 0
Cusp forms 238 238 0
Eisenstein series 8 8 0

Trace form

\( 238 q - 2 q^{2} + q^{3} + 230 q^{4} - 2 q^{5} - 3 q^{6} + 2 q^{7} - 12 q^{8} - 120 q^{9} + O(q^{10}) \) \( 238 q - 2 q^{2} + q^{3} + 230 q^{4} - 2 q^{5} - 3 q^{6} + 2 q^{7} - 12 q^{8} - 120 q^{9} + 13 q^{12} - 22 q^{13} - 16 q^{14} + 2 q^{15} + 198 q^{16} - 4 q^{17} + 3 q^{18} + 2 q^{19} - 11 q^{20} - 5 q^{21} - 8 q^{23} - 42 q^{24} - 109 q^{25} + 8 q^{26} - 20 q^{27} + 16 q^{28} - 6 q^{29} + 15 q^{30} - 32 q^{31} - 26 q^{32} + 6 q^{33} - 34 q^{34} + 9 q^{35} - 130 q^{36} - 9 q^{37} - 14 q^{38} - 3 q^{39} - 12 q^{40} + 26 q^{41} - 14 q^{42} + 10 q^{43} - 16 q^{44} - 24 q^{46} - 8 q^{47} + 10 q^{48} + 196 q^{49} + 63 q^{50} + 13 q^{51} - 98 q^{52} + 11 q^{53} + 48 q^{54} + 20 q^{55} - 40 q^{56} - 12 q^{57} - 70 q^{58} + 4 q^{59} + 26 q^{60} - 9 q^{61} - 78 q^{62} - q^{63} + 168 q^{64} + 38 q^{65} + 180 q^{66} + 6 q^{67} - 40 q^{68} + 33 q^{69} + 8 q^{70} - 46 q^{71} + 13 q^{72} + 52 q^{73} + 9 q^{74} - 48 q^{75} + 44 q^{76} - 5 q^{77} + 65 q^{78} - 36 q^{79} - 69 q^{80} - 123 q^{81} + 8 q^{82} - 17 q^{83} - 55 q^{84} - 7 q^{85} + 40 q^{86} + 7 q^{87} + 34 q^{88} - 2 q^{89} + 84 q^{90} - q^{91} + 4 q^{92} + 3 q^{93} + 88 q^{94} + 41 q^{95} - 101 q^{96} - 28 q^{97} - 102 q^{98} + 67 q^{99} + O(q^{100}) \)

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.