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Properties

Label 2015.2.ej
Level $2015$
Weight $2$
Character orbit 2015.ej
Rep. character $\chi_{2015}(8,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1760$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 2015 = 5 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2015.ej (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2015 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(448\)

Dimensions

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

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

Trace form

\( 1760 q - 12 q^{2} - 12 q^{3} - 432 q^{4} - 16 q^{5} - 32 q^{6} + 4 q^{8} + O(q^{10}) \) \( 1760 q - 12 q^{2} - 12 q^{3} - 432 q^{4} - 16 q^{5} - 32 q^{6} + 4 q^{8} - 24 q^{10} - 12 q^{11} - 24 q^{12} - 6 q^{13} + 12 q^{15} - 440 q^{16} - 16 q^{19} - 52 q^{20} - 36 q^{21} + 48 q^{22} - 8 q^{23} + 40 q^{24} + 8 q^{25} - 32 q^{26} - 32 q^{30} - 32 q^{31} - 24 q^{32} - 60 q^{33} + 16 q^{34} + 12 q^{35} + 16 q^{38} - 16 q^{39} + 20 q^{40} - 20 q^{41} - 60 q^{42} + 8 q^{43} + 40 q^{44} + 56 q^{45} + 12 q^{46} + 44 q^{48} + 392 q^{49} - 84 q^{50} - 56 q^{52} - 24 q^{53} - 8 q^{54} + 12 q^{55} - 16 q^{57} - 24 q^{59} + 16 q^{60} - 64 q^{61} - 40 q^{62} - 288 q^{63} - 432 q^{64} + 34 q^{65} - 40 q^{66} + 16 q^{69} + 82 q^{70} - 60 q^{71} - 12 q^{73} + 56 q^{75} + 116 q^{76} - 128 q^{77} - 56 q^{78} + 24 q^{80} + 384 q^{81} + 16 q^{82} - 36 q^{85} - 28 q^{86} - 104 q^{87} + 196 q^{90} - 20 q^{91} - 32 q^{92} + 8 q^{95} - 52 q^{96} - 132 q^{97} - 72 q^{98} + 24 q^{99} + O(q^{100}) \)

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.