Properties

Label 2015.2.cp
Level 2015
Weight 2
Character orbit cp
Rep. character \(\chi_{2015}(32,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 840
Sturm bound 448

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Defining parameters

Level: \( N \) = \( 2015 = 5 \cdot 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2015.cp (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 65 \)
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 912 840 72
Cusp forms 880 840 40
Eisenstein series 32 0 32

Trace form

\( 840q + 4q^{2} - 420q^{4} + 4q^{5} - 24q^{8} + 24q^{9} + O(q^{10}) \) \( 840q + 4q^{2} - 420q^{4} + 4q^{5} - 24q^{8} + 24q^{9} + 16q^{11} - 32q^{12} - 12q^{13} - 8q^{15} - 420q^{16} + 8q^{17} - 8q^{19} + 8q^{20} - 8q^{21} - 16q^{22} - 16q^{23} + 32q^{24} + 20q^{25} + 32q^{26} + 28q^{32} + 32q^{33} + 20q^{34} - 96q^{36} - 96q^{37} - 8q^{39} + 48q^{40} - 20q^{41} + 120q^{42} + 40q^{43} - 72q^{44} - 100q^{45} + 8q^{46} - 124q^{48} + 428q^{49} + 4q^{50} - 40q^{52} - 12q^{53} - 32q^{54} - 68q^{55} + 72q^{56} - 96q^{57} + 168q^{58} + 16q^{59} + 148q^{60} + 24q^{61} - 36q^{63} + 840q^{64} - 12q^{65} + 96q^{67} - 4q^{68} + 8q^{69} - 136q^{70} + 48q^{71} + 144q^{72} - 160q^{73} + 36q^{74} - 32q^{75} + 80q^{76} - 64q^{77} - 164q^{78} + 44q^{80} + 428q^{81} - 40q^{82} - 80q^{84} + 4q^{85} - 104q^{86} - 128q^{87} - 112q^{88} - 12q^{89} + 108q^{90} + 16q^{91} + 96q^{92} - 32q^{95} - 48q^{96} + 40q^{97} + 32q^{98} + 144q^{99} + O(q^{100}) \)

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

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