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Properties

Label 2015.2.de
Level $2015$
Weight $2$
Character orbit 2015.de
Rep. character $\chi_{2015}(88,\cdot)$
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.de (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

\( 880 q - 12 q^{2} - 12 q^{6} - 6 q^{7} + O(q^{10}) \) \( 880 q - 12 q^{2} - 12 q^{6} - 6 q^{7} + 2 q^{10} - 12 q^{11} - 42 q^{12} - 6 q^{13} + 400 q^{16} - 6 q^{17} + 48 q^{18} - 24 q^{21} - 12 q^{23} - 4 q^{25} - 12 q^{26} + 30 q^{30} - 90 q^{32} - 48 q^{33} - 22 q^{35} - 364 q^{36} - 12 q^{37} - 24 q^{38} - 22 q^{40} + 12 q^{41} - 30 q^{42} - 18 q^{43} + 114 q^{45} - 24 q^{46} + 114 q^{48} - 16 q^{51} - 30 q^{52} - 12 q^{53} - 60 q^{56} + 72 q^{60} + 48 q^{61} + 24 q^{62} + 48 q^{63} + 12 q^{65} - 128 q^{66} + 18 q^{67} + 62 q^{78} + 24 q^{80} - 696 q^{81} - 20 q^{82} + 102 q^{83} - 24 q^{85} - 6 q^{87} - 78 q^{88} + 56 q^{90} - 24 q^{91} + 48 q^{93} - 26 q^{95} + 120 q^{96} - 48 q^{97} + O(q^{100}) \)

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.