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Properties

Label 1339.2.u
Level $1339$
Weight $2$
Character orbit 1339.u
Rep. character $\chi_{1339}(571,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $240$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1339 = 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1339.u (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 248 248 0
Cusp forms 240 240 0
Eisenstein series 8 8 0

Trace form

\( 240 q - 4 q^{3} + 118 q^{4} + 244 q^{9} + O(q^{10}) \) \( 240 q - 4 q^{3} + 118 q^{4} + 244 q^{9} - 32 q^{10} - 20 q^{12} - 12 q^{13} - 24 q^{14} - 110 q^{16} - 4 q^{17} - 24 q^{22} - 16 q^{23} + 110 q^{25} + 28 q^{26} - 16 q^{27} - 6 q^{29} - 36 q^{30} - 42 q^{35} + 154 q^{36} + 24 q^{38} - 6 q^{39} - 32 q^{40} - 4 q^{42} + 80 q^{48} + 114 q^{49} - 24 q^{51} - 37 q^{52} - 18 q^{53} + 36 q^{55} - 34 q^{56} - 8 q^{61} + 38 q^{62} - 184 q^{64} - 5 q^{65} - 28 q^{66} + 94 q^{68} - 36 q^{69} - 28 q^{74} - 12 q^{75} + 8 q^{77} + 34 q^{78} - 32 q^{79} + 272 q^{81} - 12 q^{82} + 12 q^{87} + 32 q^{88} - 232 q^{90} - 8 q^{91} - 72 q^{92} - 128 q^{95} + O(q^{100}) \)

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.