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Properties

Label 2015.2.dz
Level $2015$
Weight $2$
Character orbit 2015.dz
Rep. character $\chi_{2015}(838,\cdot)$
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.dz (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

\( 840 q + 420 q^{4} - 8 q^{5} - 24 q^{9} + O(q^{10}) \) \( 840 q + 420 q^{4} - 8 q^{5} - 24 q^{9} + 16 q^{11} + 32 q^{12} + 8 q^{15} - 420 q^{16} - 20 q^{17} - 8 q^{18} + 8 q^{19} + 20 q^{20} - 8 q^{21} - 16 q^{22} + 16 q^{23} - 32 q^{24} - 20 q^{25} + 32 q^{26} + 24 q^{33} - 20 q^{34} - 96 q^{36} + 28 q^{37} + 8 q^{39} + 48 q^{40} - 20 q^{41} - 120 q^{42} - 40 q^{43} + 72 q^{44} - 20 q^{45} + 8 q^{46} + 188 q^{48} - 428 q^{49} + 4 q^{50} + 96 q^{52} - 12 q^{53} + 32 q^{54} + 4 q^{55} + 72 q^{56} - 20 q^{58} - 16 q^{59} - 52 q^{60} + 24 q^{61} + 12 q^{63} - 840 q^{64} - 48 q^{65} - 96 q^{67} - 40 q^{68} - 8 q^{69} - 8 q^{70} + 48 q^{71} - 12 q^{72} - 36 q^{74} + 32 q^{75} + 80 q^{76} + 64 q^{77} - 204 q^{78} + 12 q^{80} + 428 q^{81} - 140 q^{82} + 24 q^{83} + 80 q^{84} + 124 q^{85} - 104 q^{86} + 64 q^{87} - 176 q^{88} + 12 q^{89} - 108 q^{90} + 16 q^{91} + 96 q^{92} + 32 q^{95} - 48 q^{96} + 132 q^{98} - 144 q^{99} + O(q^{100}) \)

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

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