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Properties

Label 2015.2.dn
Level $2015$
Weight $2$
Character orbit 2015.dn
Rep. character $\chi_{2015}(192,\cdot)$
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.dn (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

\( 880 q - 12 q^{2} - 6 q^{3} - 24 q^{6} + O(q^{10}) \) \( 880 q - 12 q^{2} - 6 q^{3} - 24 q^{6} - 4 q^{10} - 24 q^{11} - 42 q^{12} - 6 q^{13} + 400 q^{16} - 48 q^{18} - 30 q^{20} + 24 q^{21} - 60 q^{22} + 12 q^{23} - 4 q^{25} - 12 q^{26} + 6 q^{28} - 30 q^{30} - 90 q^{32} - 48 q^{33} - 22 q^{35} + 728 q^{36} - 6 q^{37} - 24 q^{38} - 22 q^{40} + 24 q^{46} - 90 q^{50} - 16 q^{51} - 72 q^{52} - 12 q^{53} - 6 q^{55} + 120 q^{56} - 72 q^{60} - 48 q^{61} + 54 q^{62} + 48 q^{63} - 12 q^{65} - 128 q^{66} - 66 q^{68} - 12 q^{71} - 150 q^{72} + 84 q^{76} + 62 q^{78} + 348 q^{81} + 10 q^{82} - 102 q^{83} + 24 q^{85} + 12 q^{87} + 56 q^{90} + 24 q^{91} + 30 q^{93} - 26 q^{95} - 120 q^{96} - 48 q^{97} - 90 q^{98} + O(q^{100}) \)

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.