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Properties

Label 2015.2.gc
Level $2015$
Weight $2$
Character orbit 2015.gc
Rep. character $\chi_{2015}(7,\cdot)$
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.gc (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

\( 3520 q - 18 q^{2} - 6 q^{3} - 432 q^{4} - 8 q^{5} - 16 q^{6} - 12 q^{7} + O(q^{10}) \) \( 3520 q - 18 q^{2} - 6 q^{3} - 432 q^{4} - 8 q^{5} - 16 q^{6} - 12 q^{7} - 60 q^{10} - 36 q^{11} + 6 q^{12} - 18 q^{13} - 24 q^{14} + 6 q^{15} + 404 q^{16} - 24 q^{17} - 50 q^{18} + 8 q^{19} - 142 q^{20} - 12 q^{21} + 24 q^{22} - 14 q^{23} - 20 q^{24} + 8 q^{25} - 16 q^{26} - 72 q^{27} - 46 q^{28} - 44 q^{30} - 16 q^{31} - 66 q^{32} + 18 q^{33} + 112 q^{34} - 114 q^{35} - 48 q^{36} - 40 q^{37} + 112 q^{38} - 16 q^{39} - 32 q^{40} - 28 q^{41} - 24 q^{42} - 28 q^{43} + 40 q^{44} + 76 q^{45} - 48 q^{46} - 56 q^{47} - 44 q^{48} + 392 q^{49} + 60 q^{50} + 24 q^{51} + 32 q^{52} - 24 q^{53} - 8 q^{54} - 30 q^{55} - 96 q^{56} - 36 q^{57} + 10 q^{58} + 24 q^{59} + 32 q^{60} - 32 q^{61} + 14 q^{62} + 138 q^{63} + 720 q^{64} + 2 q^{65} - 104 q^{66} - 48 q^{68} + 40 q^{69} - 26 q^{70} - 132 q^{71} - 166 q^{72} + 20 q^{75} + 220 q^{76} + 184 q^{77} + 12 q^{78} + 288 q^{79} + 34 q^{80} + 708 q^{81} - 14 q^{82} - 10 q^{83} - 24 q^{84} - 102 q^{85} - 44 q^{86} - 28 q^{87} - 24 q^{88} - 104 q^{90} - 16 q^{91} - 64 q^{92} + 42 q^{93} + 24 q^{94} - 22 q^{95} - 284 q^{96} - 234 q^{97} + 24 q^{99} + O(q^{100}) \)

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.