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Properties

Label 2015.2.bs
Level $2015$
Weight $2$
Character orbit 2015.bs
Rep. character $\chi_{2015}(94,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $416$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 2015 = 5 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2015.bs (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 456 416 40
Cusp forms 440 416 24
Eisenstein series 16 0 16

Trace form

\( 416 q + 204 q^{4} + 4 q^{5} + 196 q^{9} + O(q^{10}) \) \( 416 q + 204 q^{4} + 4 q^{5} + 196 q^{9} - 12 q^{10} - 4 q^{11} + 40 q^{14} + 12 q^{15} - 180 q^{16} - 20 q^{19} + 4 q^{20} - 8 q^{21} - 16 q^{24} + 4 q^{25} - 16 q^{26} - 8 q^{29} - 16 q^{30} - 10 q^{35} - 148 q^{36} + 36 q^{39} - 80 q^{40} - 24 q^{41} - 8 q^{44} - 48 q^{46} + 188 q^{49} + 36 q^{50} - 72 q^{51} + 84 q^{54} + 34 q^{55} + 60 q^{56} + 24 q^{59} + 244 q^{60} - 24 q^{61} - 392 q^{64} - 8 q^{65} - 32 q^{66} - 20 q^{69} - 136 q^{70} + 20 q^{71} - 12 q^{74} + 36 q^{75} + 44 q^{76} + 16 q^{79} - 46 q^{80} - 184 q^{81} - 204 q^{84} - 18 q^{85} - 104 q^{86} - 44 q^{89} - 116 q^{90} - 100 q^{94} - 28 q^{95} + 128 q^{96} - 96 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2015, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)