Properties

Label 1339.2.bt
Level $1339$
Weight $2$
Character orbit 1339.bt
Rep. character $\chi_{1339}(23,\cdot)$
Character field $\Q(\zeta_{102})$
Dimension $3840$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1339 = 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1339.bt (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 3968 3968 0
Cusp forms 3840 3840 0
Eisenstein series 128 128 0

Trace form

\( 3840 q - 45 q^{2} - 13 q^{3} - 135 q^{4} - 45 q^{6} - 51 q^{7} + 99 q^{9} + O(q^{10}) \) \( 3840 q - 45 q^{2} - 13 q^{3} - 135 q^{4} - 45 q^{6} - 51 q^{7} + 99 q^{9} - 83 q^{10} - 51 q^{11} + 64 q^{12} - 22 q^{13} - 44 q^{14} - 63 q^{15} + 93 q^{16} - 13 q^{17} - 39 q^{19} - 69 q^{20} - 23 q^{22} - 13 q^{23} - 3 q^{24} + 164 q^{25} - 44 q^{26} - 88 q^{27} + 240 q^{28} - 11 q^{29} - 5 q^{30} - 99 q^{32} - 57 q^{33} - 5 q^{35} - 265 q^{36} - 39 q^{37} - 74 q^{38} + 84 q^{39} - 84 q^{40} - 45 q^{41} + 11 q^{42} - 5 q^{43} - 75 q^{45} + 120 q^{46} - 61 q^{48} - 125 q^{49} - 9 q^{50} - 8 q^{51} - 78 q^{52} - 104 q^{53} - 129 q^{54} - 23 q^{55} + 100 q^{56} - 9 q^{58} - 3 q^{59} - 21 q^{61} - 55 q^{62} - 45 q^{63} - 220 q^{64} - 50 q^{65} - 276 q^{66} - 63 q^{67} - 254 q^{68} - 141 q^{69} - 75 q^{71} - 3 q^{72} + 5 q^{74} - 11 q^{75} - 69 q^{76} + 132 q^{77} - 74 q^{78} - 60 q^{79} - 159 q^{80} + 95 q^{81} - 64 q^{82} - 129 q^{84} + 75 q^{85} - 11 q^{87} - 149 q^{88} - 9 q^{89} - 28 q^{90} + 206 q^{91} - 160 q^{92} + 303 q^{93} + 91 q^{94} - 93 q^{95} + 231 q^{97} + 342 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1339, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.