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Properties

Label 1339.2.bp
Level $1339$
Weight $2$
Character orbit 1339.bp
Rep. character $\chi_{1339}(25,\cdot)$
Character field $\Q(\zeta_{102})$
Dimension $3840$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1339 = 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1339.bp (of order \(102\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1339 \)
Character field: \(\Q(\zeta_{102})\)
Sturm bound: \(242\)

Dimensions

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

Total New Old
Modular forms 3968 3968 0
Cusp forms 3840 3840 0
Eisenstein series 128 128 0

Trace form

\( 3840 q - 64 q^{3} - 186 q^{4} - 312 q^{9} + O(q^{10}) \) \( 3840 q - 64 q^{3} - 186 q^{4} - 312 q^{9} - 104 q^{10} - 116 q^{12} - 22 q^{13} - 44 q^{14} + 42 q^{16} - 64 q^{17} - 44 q^{22} - 52 q^{23} - 178 q^{25} - 62 q^{26} - 52 q^{27} - 62 q^{29} - 32 q^{30} - 26 q^{35} + 50 q^{36} - 92 q^{38} + 108 q^{39} - 36 q^{40} - 64 q^{42} - 68 q^{43} - 148 q^{48} - 182 q^{49} - 44 q^{51} + 3 q^{52} - 50 q^{53} - 104 q^{55} - 170 q^{56} - 60 q^{61} - 106 q^{62} + 320 q^{64} - 29 q^{65} + 96 q^{66} + 280 q^{68} - 168 q^{69} - 40 q^{74} - 56 q^{75} + 60 q^{77} - 170 q^{78} - 36 q^{79} - 340 q^{81} - 124 q^{82} - 80 q^{87} + 172 q^{88} + 164 q^{90} - 43 q^{91} - 64 q^{92} - 272 q^{94} + 60 q^{95} + O(q^{100}) \)

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.