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Properties

Label 1339.2.bs
Level $1339$
Weight $2$
Character orbit 1339.bs
Rep. character $\chi_{1339}(4,\cdot)$
Character field $\Q(\zeta_{102})$
Dimension $3808$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1339 = 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1339.bs (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 3936 3936 0
Cusp forms 3808 3808 0
Eisenstein series 128 128 0

Trace form

\( 3808 q - 48 q^{2} - 12 q^{3} - 134 q^{4} - 51 q^{6} - 54 q^{7} + 95 q^{9} + O(q^{10}) \) \( 3808 q - 48 q^{2} - 12 q^{3} - 134 q^{4} - 51 q^{6} - 54 q^{7} + 95 q^{9} - 89 q^{10} - 51 q^{11} - 141 q^{12} - 30 q^{13} - 68 q^{14} - 51 q^{15} + 86 q^{16} - 19 q^{17} - 3 q^{18} - 51 q^{19} - 51 q^{20} - 3 q^{21} - 5 q^{22} - 13 q^{23} - 21 q^{24} - 177 q^{25} - 8 q^{26} - 96 q^{27} - 345 q^{28} - 20 q^{29} - 38 q^{30} - 30 q^{32} - 54 q^{33} - 306 q^{34} - 23 q^{35} + 435 q^{36} - 60 q^{37} - 68 q^{38} + 101 q^{39} - 60 q^{40} - 48 q^{41} - 7 q^{42} + 35 q^{43} - 48 q^{44} - 63 q^{45} + 6 q^{47} - 129 q^{48} - 117 q^{49} - 51 q^{50} - 113 q^{51} - 34 q^{52} - 59 q^{53} + 27 q^{54} - 29 q^{55} + 82 q^{56} - 12 q^{57} - 30 q^{58} - 51 q^{59} - 597 q^{60} - 22 q^{61} - 22 q^{62} - 51 q^{63} + 288 q^{64} - 47 q^{65} + 48 q^{66} - 51 q^{67} - 200 q^{68} - 198 q^{69} + 36 q^{70} - 18 q^{71} - 138 q^{72} + 41 q^{74} - 63 q^{75} + 69 q^{76} - 153 q^{77} - 128 q^{78} - 112 q^{79} - 132 q^{80} + 82 q^{81} + 113 q^{82} - 15 q^{83} - 425 q^{84} + 51 q^{85} + 42 q^{86} - 131 q^{87} - 5 q^{88} - 9 q^{89} - 88 q^{90} - 147 q^{91} + 2 q^{92} - 450 q^{93} + 49 q^{94} - 24 q^{95} + 171 q^{96} + 17 q^{97} + 372 q^{98} - 75 q^{99} + O(q^{100}) \)

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.