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Properties

Label 1339.2.cc
Level $1339$
Weight $2$
Character orbit 1339.cc
Rep. character $\chi_{1339}(45,\cdot)$
Character field $\Q(\zeta_{204})$
Dimension $7616$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1339 = 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1339.cc (of order \(204\) and degree \(64\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1339 \)
Character field: \(\Q(\zeta_{204})\)
Sturm bound: \(242\)

Dimensions

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

Total New Old
Modular forms 7872 7872 0
Cusp forms 7616 7616 0
Eisenstein series 256 256 0

Trace form

\( 7616 q - 66 q^{2} - 34 q^{3} - 96 q^{4} - 62 q^{5} - 62 q^{6} - 62 q^{7} - 64 q^{8} - 258 q^{9} + O(q^{10}) \) \( 7616 q - 66 q^{2} - 34 q^{3} - 96 q^{4} - 62 q^{5} - 62 q^{6} - 62 q^{7} - 64 q^{8} - 258 q^{9} - 102 q^{10} - 80 q^{11} + 26 q^{12} - 78 q^{13} - 120 q^{14} - 68 q^{15} - 272 q^{16} - 90 q^{17} - 50 q^{18} - 68 q^{19} - 62 q^{20} - 42 q^{21} - 10 q^{22} - 66 q^{23} - 8 q^{24} - 12 q^{25} - 20 q^{26} - 136 q^{27} + 332 q^{28} - 40 q^{29} - 138 q^{30} - 96 q^{31} - 88 q^{32} - 64 q^{33} + 342 q^{34} - 34 q^{35} - 102 q^{36} - 88 q^{37} - 30 q^{38} + 142 q^{39} - 124 q^{40} - 52 q^{41} - 10 q^{42} - 182 q^{43} - 56 q^{44} - 44 q^{45} - 152 q^{46} - 84 q^{47} - 34 q^{48} - 168 q^{49} - 170 q^{50} - 6 q^{51} - 60 q^{52} - 142 q^{53} - 158 q^{54} - 100 q^{55} - 54 q^{56} - 50 q^{57} - 34 q^{58} - 60 q^{59} - 864 q^{60} - 30 q^{61} - 126 q^{62} - 114 q^{63} - 140 q^{65} - 16 q^{66} - 60 q^{67} - 394 q^{68} - 180 q^{69} - 20 q^{70} + 122 q^{71} - 64 q^{72} - 112 q^{73} - 34 q^{74} - 32 q^{75} - 24 q^{76} + 408 q^{77} - 26 q^{78} - 96 q^{79} - 80 q^{80} + 148 q^{81} - 96 q^{82} - 74 q^{83} + 66 q^{84} - 46 q^{85} - 6 q^{86} - 34 q^{87} - 174 q^{88} - 32 q^{89} + 48 q^{91} - 128 q^{92} - 542 q^{93} + 246 q^{94} - 102 q^{95} + 604 q^{96} - 498 q^{97} - 232 q^{98} + 180 q^{99} + O(q^{100}) \)

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.