↑

Properties

Label 1339.2.bg
Level $1339$
Weight $2$
Character orbit 1339.bg
Rep. character $\chi_{1339}(64,\cdot)$
Character field $\Q(\zeta_{34})$
Dimension $1888$
Sturm bound $242$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1339 = 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1339.bg (of order \(34\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1339 \)
Character field: \(\Q(\zeta_{34})\)
Sturm bound: \(242\)

Dimensions

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

Total New Old
Modular forms 1952 1952 0
Cusp forms 1888 1888 0
Eisenstein series 64 64 0

Trace form

\( 1888 q - 34 q^{3} + 82 q^{4} - 148 q^{9} + O(q^{10}) \) \( 1888 q - 34 q^{3} + 82 q^{4} - 148 q^{9} + 26 q^{10} + 46 q^{12} - 19 q^{13} - 46 q^{14} - 130 q^{16} - 26 q^{17} - 58 q^{22} - 26 q^{23} + 80 q^{25} + 2 q^{26} - 34 q^{27} - 22 q^{29} - 22 q^{30} - 58 q^{35} - 214 q^{36} - 76 q^{38} - 121 q^{39} - 30 q^{40} - 14 q^{42} - 30 q^{43} - 46 q^{48} + 88 q^{49} - 10 q^{51} - 7 q^{52} - 34 q^{53} - 22 q^{55} + 116 q^{56} - 70 q^{61} - 62 q^{62} - 142 q^{64} - q^{65} - 186 q^{66} - 490 q^{68} + 162 q^{69} - 86 q^{74} - 14 q^{75} - 174 q^{77} + 5 q^{78} - 34 q^{79} - 72 q^{81} + 4 q^{82} - 34 q^{87} + 146 q^{88} - 50 q^{90} + 207 q^{91} + 22 q^{92} + 50 q^{94} - 54 q^{95} + O(q^{100}) \)

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.