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Properties

Label 2015.2.do
Level $2015$
Weight $2$
Character orbit 2015.do
Rep. character $\chi_{2015}(161,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $592$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 2015 = 5 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2015.do (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 403 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 912 592 320
Cusp forms 880 592 288
Eisenstein series 32 0 32

Trace form

\( 592 q + 36 q^{6} + 4 q^{7} + 24 q^{8} + 288 q^{9} + O(q^{10}) \) \( 592 q + 36 q^{6} + 4 q^{7} + 24 q^{8} + 288 q^{9} + 12 q^{11} - 24 q^{14} - 544 q^{16} + 44 q^{18} - 4 q^{19} + 8 q^{20} + 48 q^{21} - 24 q^{22} - 72 q^{24} + 24 q^{26} - 52 q^{31} + 88 q^{32} + 32 q^{33} + 12 q^{34} + 12 q^{37} - 8 q^{39} + 4 q^{41} + 132 q^{44} - 8 q^{45} - 96 q^{52} - 72 q^{53} + 156 q^{57} - 24 q^{59} - 24 q^{63} + 272 q^{66} - 8 q^{67} + 72 q^{68} + 16 q^{70} + 8 q^{71} - 136 q^{72} - 36 q^{73} - 120 q^{74} - 56 q^{76} - 32 q^{78} - 144 q^{79} + 16 q^{80} - 312 q^{81} - 12 q^{83} + 144 q^{84} + 120 q^{86} - 16 q^{87} + 240 q^{93} + 32 q^{94} - 384 q^{96} + 8 q^{97} + 20 q^{98} + 120 q^{99} + O(q^{100}) \)

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

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