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Properties

Label 2015.2.hc
Level $2015$
Weight $2$
Character orbit 2015.hc
Rep. character $\chi_{2015}(24,\cdot)$
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.hc (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

\( 3520 q - 36 q^{4} - 8 q^{5} - 48 q^{6} + 400 q^{9} + O(q^{10}) \) \( 3520 q - 36 q^{4} - 8 q^{5} - 48 q^{6} + 400 q^{9} - 30 q^{10} - 28 q^{11} - 88 q^{14} + 22 q^{15} - 428 q^{16} - 44 q^{19} - 8 q^{20} + 28 q^{21} - 116 q^{24} - 48 q^{26} + 4 q^{29} - 16 q^{31} - 124 q^{34} + 14 q^{35} - 52 q^{39} - 28 q^{40} - 16 q^{41} + 12 q^{44} + 44 q^{45} - 60 q^{49} - 42 q^{50} - 96 q^{51} + 92 q^{54} - 4 q^{55} - 28 q^{59} + 16 q^{60} - 144 q^{65} - 16 q^{66} - 60 q^{69} + 142 q^{70} - 116 q^{71} - 20 q^{74} - 228 q^{75} - 80 q^{76} - 64 q^{79} - 124 q^{80} + 356 q^{81} - 220 q^{84} + 52 q^{85} + 92 q^{86} - 40 q^{89} - 126 q^{90} - 56 q^{91} - 32 q^{94} + 42 q^{95} - 40 q^{96} - 48 q^{99} + O(q^{100}) \)

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.