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Properties

Label 2015.2.eg
Level $2015$
Weight $2$
Character orbit 2015.eg
Rep. character $\chi_{2015}(16,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $1184$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 2015 = 5 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2015.eg (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 403 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 1824 1184 640
Cusp forms 1760 1184 576
Eisenstein series 64 0 64

Trace form

\( 1184 q + 4 q^{3} + 144 q^{4} - 12 q^{6} + 4 q^{7} - 36 q^{8} + 144 q^{9} + O(q^{10}) \) \( 1184 q + 4 q^{3} + 144 q^{4} - 12 q^{6} + 4 q^{7} - 36 q^{8} + 144 q^{9} + 6 q^{11} - 52 q^{12} - 2 q^{13} + 40 q^{14} + 128 q^{16} - 16 q^{18} + 4 q^{19} - 8 q^{20} - 100 q^{21} + 16 q^{22} + 22 q^{23} - 24 q^{24} + 1184 q^{25} + 4 q^{26} + 16 q^{27} - 36 q^{28} + 8 q^{29} - 32 q^{30} + 96 q^{31} + 56 q^{32} - 16 q^{33} + 136 q^{34} - 524 q^{36} + 12 q^{37} - 48 q^{39} - 16 q^{41} + 42 q^{43} - 72 q^{44} + 8 q^{45} - 4 q^{46} - 48 q^{47} - 44 q^{48} + 108 q^{49} + 40 q^{51} - 86 q^{52} - 80 q^{53} + 12 q^{54} + 28 q^{55} + 24 q^{56} - 288 q^{57} - 84 q^{58} + 52 q^{59} - 4 q^{61} - 12 q^{62} + 72 q^{63} - 244 q^{64} + 32 q^{66} - 12 q^{67} - 212 q^{68} + 120 q^{69} + 16 q^{70} - 72 q^{71} - 88 q^{72} + 88 q^{73} - 20 q^{74} + 4 q^{75} - 40 q^{76} + 8 q^{77} + 66 q^{78} + 32 q^{79} + 24 q^{80} + 228 q^{81} - 112 q^{82} + 8 q^{83} - 168 q^{84} - 360 q^{86} + 20 q^{87} - 132 q^{88} - 48 q^{89} + 48 q^{90} + 42 q^{91} + 728 q^{92} + 42 q^{93} + 36 q^{94} - 4 q^{95} - 208 q^{96} - 44 q^{97} - 180 q^{98} - 120 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(2015, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2015, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(403, [\chi])\)\(^{\oplus 2}\)