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Properties

Label 1339.2.c
Level $1339$
Weight $2$
Character orbit 1339.c
Rep. character $\chi_{1339}(207,\cdot)$
Character field $\Q$
Dimension $118$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1339 = 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1339.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Sturm bound: \(242\)

Dimensions

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

Total New Old
Modular forms 122 118 4
Cusp forms 118 118 0
Eisenstein series 4 0 4

Trace form

\( 118 q - 116 q^{4} + 114 q^{9} + O(q^{10}) \) \( 118 q - 116 q^{4} + 114 q^{9} + 8 q^{10} - 12 q^{12} + 2 q^{13} + 12 q^{14} + 96 q^{16} - 8 q^{17} + 24 q^{22} - 8 q^{23} - 114 q^{25} - 19 q^{26} - 12 q^{29} - 12 q^{30} + 24 q^{35} - 92 q^{36} + 42 q^{38} - 32 q^{39} - 4 q^{40} - 20 q^{42} - 4 q^{43} + 12 q^{48} - 122 q^{49} - 24 q^{51} - 10 q^{52} - 12 q^{55} - 14 q^{56} + 36 q^{61} + 28 q^{62} - 96 q^{64} - 16 q^{65} + 16 q^{66} + 14 q^{68} - 60 q^{69} + 52 q^{74} - 20 q^{75} + 4 q^{77} + 80 q^{78} + 38 q^{81} + 30 q^{82} - 44 q^{88} + 16 q^{90} + 14 q^{91} + 12 q^{92} - 84 q^{94} + 20 q^{95} + O(q^{100}) \)

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.