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Properties

Label 1339.2.i
Level $1339$
Weight $2$
Character orbit 1339.i
Rep. character $\chi_{1339}(411,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $236$
Sturm bound $242$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 244 244 0
Cusp forms 236 236 0
Eisenstein series 8 8 0

Trace form

\( 236 q - 4 q^{2} + 8 q^{7} + 4 q^{8} - 228 q^{9} + O(q^{10}) \) \( 236 q - 4 q^{2} + 8 q^{7} + 4 q^{8} - 228 q^{9} + 8 q^{13} - 8 q^{14} + 24 q^{15} - 224 q^{16} + 32 q^{19} - 54 q^{26} + 78 q^{28} - 24 q^{29} + 34 q^{32} + 16 q^{33} + 8 q^{34} - 32 q^{41} + 22 q^{46} + 72 q^{50} - 60 q^{52} + 24 q^{55} - 20 q^{58} + 8 q^{59} - 128 q^{60} - 8 q^{61} - 60 q^{63} - 176 q^{66} - 80 q^{68} + 28 q^{72} - 108 q^{76} + 88 q^{79} + 300 q^{81} + 84 q^{83} - 96 q^{91} + 32 q^{92} - 12 q^{93} + 44 q^{97} + 30 q^{98} + O(q^{100}) \)

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.