Properties

Label 2015.2.m
Level 2015
Weight 2
Character orbit m
Rep. character \(\chi_{2015}(993,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 420
Sturm bound 448

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Defining parameters

Level: \( N \) = \( 2015 = 5 \cdot 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2015.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 65 \)
Character field: \(\Q(i)\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 456 420 36
Cusp forms 440 420 20
Eisenstein series 16 0 16

Trace form

\( 420q - 420q^{4} + 8q^{5} + O(q^{10}) \) \( 420q - 420q^{4} + 8q^{5} - 16q^{11} + 16q^{12} - 24q^{13} - 8q^{15} + 420q^{16} - 28q^{17} - 52q^{18} - 8q^{19} - 20q^{20} + 8q^{21} + 16q^{22} + 32q^{23} + 32q^{24} + 20q^{25} - 32q^{26} + 20q^{34} + 56q^{37} - 8q^{39} - 96q^{40} - 4q^{41} + 16q^{43} + 24q^{44} - 40q^{45} - 8q^{46} - 32q^{48} + 356q^{49} - 52q^{50} + 36q^{52} + 12q^{53} - 32q^{54} - 64q^{55} - 40q^{58} - 8q^{59} + 76q^{60} - 420q^{64} - 48q^{65} - 44q^{68} + 32q^{69} + 152q^{70} - 24q^{71} + 156q^{72} - 32q^{75} - 8q^{76} + 32q^{77} - 24q^{78} + 120q^{80} - 404q^{81} - 52q^{82} - 24q^{83} + 40q^{84} - 100q^{85} + 104q^{86} + 32q^{87} + 32q^{88} - 36q^{89} - 84q^{90} - 16q^{91} - 96q^{92} + 64q^{95} - 168q^{96} + 24q^{99} + O(q^{100}) \)

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

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