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Properties

Label 1339.2.bn
Level $1339$
Weight $2$
Character orbit 1339.bn
Rep. character $\chi_{1339}(31,\cdot)$
Character field $\Q(\zeta_{68})$
Dimension $3776$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1339 = 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1339.bn (of order \(68\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1339 \)
Character field: \(\Q(\zeta_{68})\)
Sturm bound: \(242\)

Dimensions

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

Total New Old
Modular forms 3904 3904 0
Cusp forms 3776 3776 0
Eisenstein series 128 128 0

Trace form

\( 3776 q - 30 q^{2} - 68 q^{3} - 34 q^{5} - 34 q^{6} - 42 q^{7} - 38 q^{8} + 160 q^{9} + O(q^{10}) \) \( 3776 q - 30 q^{2} - 68 q^{3} - 34 q^{5} - 34 q^{6} - 42 q^{7} - 38 q^{8} + 160 q^{9} - 34 q^{11} - 42 q^{13} - 60 q^{14} - 58 q^{15} + 156 q^{16} - 34 q^{18} - 66 q^{19} - 34 q^{20} - 34 q^{21} - 68 q^{22} - 34 q^{24} + 20 q^{26} - 68 q^{27} + 92 q^{28} - 44 q^{29} - 34 q^{31} - 68 q^{32} - 50 q^{33} + 162 q^{34} - 68 q^{35} - 34 q^{37} - 306 q^{39} - 68 q^{40} - 2 q^{41} - 68 q^{42} - 34 q^{44} - 34 q^{45} + 80 q^{46} - 68 q^{48} - 106 q^{50} + 26 q^{52} - 68 q^{53} - 34 q^{54} - 92 q^{55} - 14 q^{58} - 42 q^{59} - 348 q^{60} - 60 q^{61} + 26 q^{63} - 34 q^{65} - 164 q^{66} - 34 q^{67} - 872 q^{68} - 34 q^{70} - 170 q^{71} - 62 q^{72} - 34 q^{73} - 68 q^{74} + 74 q^{76} - 34 q^{78} - 156 q^{79} - 34 q^{80} - 368 q^{81} - 118 q^{83} + 578 q^{84} + 34 q^{85} - 102 q^{86} - 68 q^{87} - 34 q^{89} + 62 q^{91} - 100 q^{92} - 294 q^{93} - 204 q^{94} + 374 q^{96} + 364 q^{97} + 208 q^{98} - 204 q^{99} + O(q^{100}) \)

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.