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Properties

Label 1339.2.bb
Level $1339$
Weight $2$
Character orbit 1339.bb
Rep. character $\chi_{1339}(150,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $476$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1339 = 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1339.bb (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1339 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(242\)

Dimensions

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

Total New Old
Modular forms 492 492 0
Cusp forms 476 476 0
Eisenstein series 16 16 0

Trace form

\( 476 q - 2 q^{2} - 6 q^{4} - 6 q^{5} - 6 q^{6} - 6 q^{7} - 4 q^{8} + 224 q^{9} + O(q^{10}) \) \( 476 q - 2 q^{2} - 6 q^{4} - 6 q^{5} - 6 q^{6} - 6 q^{7} - 4 q^{8} + 224 q^{9} + 12 q^{11} - 26 q^{12} + 10 q^{13} - 16 q^{14} + 238 q^{16} - 12 q^{17} - 18 q^{18} - 6 q^{20} - 26 q^{21} - 24 q^{22} - 36 q^{23} - 60 q^{24} + 12 q^{25} - 48 q^{26} + 8 q^{28} + 6 q^{29} + 36 q^{30} + 28 q^{31} + 20 q^{32} - 4 q^{33} - 2 q^{34} + 20 q^{37} + 30 q^{38} + 62 q^{39} - 12 q^{40} - 16 q^{41} - 24 q^{42} + 80 q^{43} - 12 q^{44} - 24 q^{45} - 52 q^{46} - 18 q^{47} + 66 q^{49} + 102 q^{50} + 6 q^{51} - 8 q^{52} + 6 q^{53} + 90 q^{54} + 66 q^{55} - 48 q^{56} - 52 q^{57} - 34 q^{58} - 8 q^{59} - 88 q^{60} - 4 q^{61} + 24 q^{62} + 46 q^{63} + 72 q^{65} + 152 q^{66} - 8 q^{67} - 82 q^{68} + 78 q^{69} - 48 q^{70} - 54 q^{71} - 4 q^{72} + 44 q^{73} - 70 q^{75} - 44 q^{76} - 42 q^{78} - 40 q^{79} + 12 q^{80} - 182 q^{81} - 6 q^{82} + 6 q^{83} + 2 q^{84} - 90 q^{85} + 6 q^{86} + 72 q^{88} - 36 q^{89} - 116 q^{91} - 8 q^{92} - 70 q^{93} - 144 q^{94} + 144 q^{96} - 12 q^{97} - 108 q^{98} - 78 q^{99} + O(q^{100}) \)

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.