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Properties

Label 2015.2.dc
Level $2015$
Weight $2$
Character orbit 2015.dc
Rep. character $\chi_{2015}(68,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $880$
Sturm bound $448$

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Defining parameters

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

Trace form

\( 880 q - 4 q^{2} - 6 q^{3} - 4 q^{5} - 4 q^{7} - 32 q^{8} + O(q^{10}) \) \( 880 q - 4 q^{2} - 6 q^{3} - 4 q^{5} - 4 q^{7} - 32 q^{8} - 4 q^{10} - 18 q^{12} - 6 q^{13} + 416 q^{16} + 4 q^{18} + 34 q^{20} - 12 q^{22} - 12 q^{23} - 4 q^{25} - 12 q^{26} + 14 q^{28} + 30 q^{30} + 16 q^{31} + 18 q^{32} + 20 q^{33} - 10 q^{35} - 872 q^{36} - 42 q^{37} - 32 q^{38} - 2 q^{40} + 8 q^{41} - 84 q^{45} - 24 q^{46} - 8 q^{47} + 10 q^{50} - 16 q^{51} - 48 q^{52} - 12 q^{53} - 6 q^{55} - 8 q^{56} - 12 q^{57} + 48 q^{61} - 74 q^{62} + 32 q^{63} - 12 q^{65} - 32 q^{66} + 12 q^{67} - 42 q^{68} - 224 q^{70} - 60 q^{71} + 18 q^{72} - 12 q^{73} + 68 q^{76} + 70 q^{78} + 16 q^{80} + 380 q^{81} - 6 q^{82} - 114 q^{83} - 48 q^{85} + 24 q^{86} - 68 q^{87} + 8 q^{90} + 24 q^{91} + 26 q^{93} + 18 q^{95} - 40 q^{97} + 38 q^{98} + O(q^{100}) \)

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.