↑

Properties

Label 2015.2.w
Level $2015$
Weight $2$
Character orbit 2015.w
Rep. character $\chi_{2015}(187,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $420$
Sturm bound $448$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2015 = 5 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2015.w (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

\( 420 q - 4 q^{2} + 420 q^{4} - 4 q^{5} - 12 q^{8} + O(q^{10}) \) \( 420 q - 4 q^{2} + 420 q^{4} - 4 q^{5} - 12 q^{8} - 16 q^{11} - 16 q^{12} - 12 q^{13} + 8 q^{15} + 420 q^{16} + 28 q^{17} + 8 q^{19} - 8 q^{20} + 8 q^{21} + 16 q^{22} - 32 q^{23} - 32 q^{24} - 20 q^{25} - 32 q^{26} - 28 q^{32} - 56 q^{33} - 20 q^{34} + 8 q^{39} - 96 q^{40} - 4 q^{41} - 16 q^{43} - 24 q^{44} - 20 q^{45} - 8 q^{46} - 32 q^{48} - 356 q^{49} + 56 q^{50} - 8 q^{52} + 12 q^{53} + 32 q^{54} - 64 q^{55} + 96 q^{57} + 8 q^{59} - 124 q^{60} - 72 q^{63} + 420 q^{64} + 24 q^{65} - 44 q^{68} - 32 q^{69} - 8 q^{70} - 24 q^{71} + 40 q^{73} + 32 q^{75} - 8 q^{76} - 32 q^{77} - 64 q^{78} - 92 q^{80} - 404 q^{81} + 52 q^{82} - 40 q^{84} - 28 q^{85} + 104 q^{86} + 32 q^{87} - 32 q^{88} + 36 q^{89} + 84 q^{90} - 16 q^{91} - 96 q^{92} - 64 q^{95} - 168 q^{96} - 40 q^{97} - 164 q^{98} - 24 q^{99} + O(q^{100}) \)

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

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