↑

Properties

Label 1339.2.be
Level $1339$
Weight $2$
Character orbit 1339.be
Rep. character $\chi_{1339}(14,\cdot)$
Character field $\Q(\zeta_{17})$
Dimension $1664$
Sturm bound $242$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1339 = 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1339.be (of order \(17\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 103 \)
Character field: \(\Q(\zeta_{17})\)
Sturm bound: \(242\)

Dimensions

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

Total New Old
Modular forms 1952 1664 288
Cusp forms 1888 1664 224
Eisenstein series 64 0 64

Trace form

\( 1664 q - 4 q^{3} - 104 q^{4} - 8 q^{5} - 12 q^{6} - 8 q^{7} - 12 q^{8} - 116 q^{9} + O(q^{10}) \) \( 1664 q - 4 q^{3} - 104 q^{4} - 8 q^{5} - 12 q^{6} - 8 q^{7} - 12 q^{8} - 116 q^{9} + 40 q^{10} - 8 q^{11} + 24 q^{12} + 28 q^{14} - 28 q^{15} - 112 q^{16} - 4 q^{17} - 48 q^{18} + 30 q^{19} - 68 q^{20} + 28 q^{21} - 32 q^{22} + 26 q^{23} - 84 q^{24} - 20 q^{25} - 28 q^{27} - 36 q^{28} - 36 q^{29} + 76 q^{30} - 48 q^{31} - 44 q^{32} - 36 q^{33} - 32 q^{35} - 164 q^{36} + 58 q^{37} + 6 q^{38} - 8 q^{39} - 100 q^{40} - 24 q^{41} - 48 q^{42} - 24 q^{43} - 48 q^{44} + 10 q^{45} - 48 q^{46} + 268 q^{47} + 196 q^{48} - 100 q^{49} + 62 q^{50} - 48 q^{51} - 8 q^{52} - 56 q^{53} - 68 q^{54} + 34 q^{55} - 108 q^{56} + 92 q^{57} + 60 q^{58} + 24 q^{59} - 108 q^{60} - 48 q^{61} - 8 q^{62} - 92 q^{63} - 132 q^{64} - 8 q^{65} + 76 q^{66} + 50 q^{67} - 108 q^{68} + 8 q^{69} - 192 q^{70} - 88 q^{71} - 156 q^{72} + 154 q^{73} - 120 q^{74} + 348 q^{75} - 76 q^{76} - 56 q^{77} - 24 q^{78} - 84 q^{79} + 204 q^{80} - 232 q^{81} + 260 q^{82} - 80 q^{83} - 124 q^{84} - 108 q^{85} + 232 q^{86} - 72 q^{87} + 176 q^{88} - 66 q^{89} + 16 q^{90} + 44 q^{92} + 204 q^{93} - 40 q^{94} + 374 q^{95} - 248 q^{96} - 92 q^{97} - 188 q^{98} - 128 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(1339, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1339, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(103, [\chi])\)\(^{\oplus 2}\)