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Properties

Label 2015.2.fy
Level $2015$
Weight $2$
Character orbit 2015.fy
Rep. character $\chi_{2015}(28,\cdot)$
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.fy (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

\( 3520 q - 18 q^{2} - 12 q^{3} - 432 q^{4} - 8 q^{5} - 16 q^{6} - 6 q^{7} + O(q^{10}) \) \( 3520 q - 18 q^{2} - 12 q^{3} - 432 q^{4} - 8 q^{5} - 16 q^{6} - 6 q^{7} - 18 q^{10} - 36 q^{11} + 42 q^{12} - 18 q^{13} + 24 q^{14} + 6 q^{15} + 404 q^{16} - 30 q^{17} - 50 q^{18} + 8 q^{19} + 32 q^{20} - 108 q^{21} - 102 q^{22} - 14 q^{23} + 4 q^{24} + 8 q^{25} - 16 q^{26} - 72 q^{27} + 8 q^{28} - 44 q^{30} - 16 q^{31} - 66 q^{32} - 162 q^{33} + 136 q^{34} + 36 q^{35} + 20 q^{37} - 104 q^{38} - 16 q^{39} - 56 q^{40} - 28 q^{41} + 42 q^{42} - 22 q^{43} - 80 q^{44} - 56 q^{45} - 48 q^{46} - 56 q^{47} - 194 q^{48} - 784 q^{49} - 18 q^{50} - 24 q^{51} - 160 q^{52} - 24 q^{53} - 8 q^{54} + 36 q^{57} + 10 q^{58} + 24 q^{59} - 148 q^{60} - 32 q^{61} - 4 q^{62} + 138 q^{63} + 720 q^{64} + 158 q^{65} - 104 q^{66} + 36 q^{68} - 80 q^{69} - 26 q^{70} + 12 q^{71} + 128 q^{72} + 92 q^{75} - 116 q^{76} - 56 q^{77} - 258 q^{78} - 288 q^{79} - 188 q^{80} - 384 q^{81} - 32 q^{82} - 10 q^{83} + 144 q^{84} + 18 q^{85} - 44 q^{86} + 56 q^{87} + 112 q^{90} - 136 q^{91} - 64 q^{92} - 60 q^{93} + 24 q^{94} - 22 q^{95} + 52 q^{96} - 54 q^{97} + 60 q^{98} - 12 q^{99} + O(q^{100}) \)

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.