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Properties

Label 2015.2.ga
Level $2015$
Weight $2$
Character orbit 2015.ga
Rep. character $\chi_{2015}(188,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $3520$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 2015 = 5 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2015.ga (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2015 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2015, [\chi])\).

Total New Old
Modular forms 3648 3648 0
Cusp forms 3520 3520 0
Eisenstein series 128 128 0

Trace form

\( 3520 q - 18 q^{2} - 6 q^{3} - 432 q^{4} - 32 q^{5} - 64 q^{6} - 6 q^{7} + O(q^{10}) \) \( 3520 q - 18 q^{2} - 6 q^{3} - 432 q^{4} - 32 q^{5} - 64 q^{6} - 6 q^{7} - 6 q^{10} - 24 q^{11} - 24 q^{12} - 12 q^{13} - 48 q^{15} + 404 q^{16} - 18 q^{17} + 28 q^{18} + 32 q^{19} + 50 q^{20} + 24 q^{22} - 26 q^{23} - 32 q^{24} - 16 q^{25} - 64 q^{26} + 72 q^{27} - 46 q^{28} - 8 q^{30} - 40 q^{31} - 156 q^{32} + 90 q^{33} + 16 q^{34} + 60 q^{35} - 96 q^{36} - 40 q^{37} + 16 q^{38} - 16 q^{39} - 56 q^{40} - 40 q^{41} + 30 q^{42} - 10 q^{43} + 40 q^{44} - 50 q^{45} + 24 q^{46} + 40 q^{47} + 94 q^{48} + 392 q^{49} - 66 q^{50} + 14 q^{52} - 48 q^{53} + 64 q^{54} + 6 q^{55} - 192 q^{56} + 10 q^{58} + 48 q^{59} - 4 q^{60} - 32 q^{61} + 14 q^{62} - 420 q^{63} + 720 q^{64} - 34 q^{65} + 64 q^{66} - 24 q^{68} + 40 q^{69} + 22 q^{70} + 24 q^{71} + 14 q^{72} - 136 q^{75} - 152 q^{76} - 128 q^{77} + 18 q^{78} + 22 q^{80} - 420 q^{81} - 2 q^{82} + 380 q^{83} + 48 q^{85} - 56 q^{86} - 16 q^{87} - 48 q^{88} + 16 q^{90} - 112 q^{91} - 160 q^{92} - 42 q^{93} + 96 q^{94} - 10 q^{95} + 16 q^{96} + 18 q^{97} - 132 q^{98} + 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2015, [\chi])\) into newform subspaces

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