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Properties

Label 1339.2.bk
Level $1339$
Weight $2$
Character orbit 1339.bk
Rep. character $\chi_{1339}(9,\cdot)$
Character field $\Q(\zeta_{51})$
Dimension $3840$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1339 = 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1339.bk (of order \(51\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1339 \)
Character field: \(\Q(\zeta_{51})\)
Sturm bound: \(242\)

Dimensions

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

Total New Old
Modular forms 3968 3968 0
Cusp forms 3840 3840 0
Eisenstein series 128 128 0

Trace form

\( 3840 q - 15 q^{2} - 17 q^{3} + 105 q^{4} - 60 q^{5} - 23 q^{6} - 17 q^{7} - 68 q^{8} + 107 q^{9} + O(q^{10}) \) \( 3840 q - 15 q^{2} - 17 q^{3} + 105 q^{4} - 60 q^{5} - 23 q^{6} - 17 q^{7} - 68 q^{8} + 107 q^{9} + 45 q^{10} - 17 q^{11} - 192 q^{12} - 26 q^{13} - 76 q^{14} - q^{15} + 101 q^{16} - 13 q^{17} - 80 q^{18} - 17 q^{19} - 15 q^{20} - 100 q^{21} - 23 q^{22} - 9 q^{23} - 29 q^{24} - 300 q^{25} - 36 q^{26} - 56 q^{27} - 124 q^{28} - 11 q^{29} - 17 q^{30} - 52 q^{31} - 15 q^{32} - 23 q^{33} + 92 q^{34} - 17 q^{35} - 25 q^{36} - 21 q^{37} - 66 q^{38} + 76 q^{39} + 28 q^{40} - 43 q^{41} - 45 q^{42} - 13 q^{43} - 52 q^{44} - 17 q^{45} - 152 q^{46} - 104 q^{47} - 17 q^{48} + 123 q^{49} - 35 q^{50} - 72 q^{51} - 94 q^{52} - 40 q^{53} - 59 q^{54} - 7 q^{55} - 88 q^{56} - 116 q^{57} - 19 q^{58} - 9 q^{59} + 246 q^{60} - 9 q^{61} + 13 q^{62} - 11 q^{63} - 652 q^{64} - 30 q^{65} - 340 q^{66} + 15 q^{67} - 198 q^{68} + 107 q^{69} - 124 q^{70} + 147 q^{71} + 27 q^{72} - 28 q^{73} - 59 q^{74} + 5 q^{75} - 47 q^{76} + 52 q^{77} - 30 q^{78} - 108 q^{79} - 53 q^{80} + 119 q^{81} + 34 q^{82} - 195 q^{84} + q^{85} + 32 q^{86} - 27 q^{87} + 67 q^{88} + 21 q^{89} + 100 q^{90} - 290 q^{91} + 56 q^{92} - 151 q^{93} + 31 q^{94} - 25 q^{95} - 924 q^{96} + 7 q^{97} - 156 q^{98} + 98 q^{99} + O(q^{100}) \)

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.