Properties

Label 2015.2.do
Level 2015
Weight 2
Character orbit 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

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

Decomposition of \(S_{2}^{\mathrm{new}}(2015, [\chi])\) into irreducible Hecke orbits

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

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