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Properties

Label 1339.2.bc
Level $1339$
Weight $2$
Character orbit 1339.bc
Rep. character $\chi_{1339}(102,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $480$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1339 = 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1339.bc (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1339 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(242\)

Dimensions

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

Total New Old
Modular forms 496 496 0
Cusp forms 480 480 0
Eisenstein series 16 16 0

Trace form

\( 480 q - 8 q^{2} - 12 q^{4} - 16 q^{7} - 16 q^{8} + 232 q^{9} + O(q^{10}) \) \( 480 q - 8 q^{2} - 12 q^{4} - 16 q^{7} - 16 q^{8} + 232 q^{9} + 4 q^{13} - 16 q^{14} - 12 q^{15} + 252 q^{16} - 24 q^{17} - 12 q^{18} - 4 q^{19} - 36 q^{23} + 12 q^{26} - 68 q^{28} - 12 q^{29} - 108 q^{30} - 46 q^{32} - 28 q^{33} - 20 q^{34} + 48 q^{36} + 20 q^{41} - 34 q^{46} + 48 q^{49} + 48 q^{50} + 32 q^{52} + 60 q^{55} - 96 q^{56} - 88 q^{58} - 8 q^{59} + 56 q^{60} - 4 q^{61} - 100 q^{63} - 112 q^{66} - 88 q^{68} + 44 q^{72} - 16 q^{76} - 64 q^{79} - 208 q^{81} - 12 q^{82} + 60 q^{83} + 80 q^{91} + 64 q^{92} + 52 q^{93} - 112 q^{97} - 126 q^{98} + O(q^{100}) \)

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.