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Properties

Label 2015.2.ci
Level $2015$
Weight $2$
Character orbit 2015.ci
Rep. character $\chi_{2015}(242,\cdot)$
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.ci (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

\( 880 q - 4 q^{3} - 864 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{7} + O(q^{10}) \) \( 880 q - 4 q^{3} - 864 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{7} + 8 q^{10} - 4 q^{11} + 8 q^{12} - 2 q^{13} + 4 q^{15} + 800 q^{16} + 28 q^{18} - 8 q^{19} + 14 q^{20} - 12 q^{21} + 16 q^{22} + 8 q^{23} + 20 q^{24} - 8 q^{25} - 4 q^{26} - 64 q^{27} - 12 q^{28} + 80 q^{30} + 8 q^{34} + 8 q^{35} - 16 q^{37} + 8 q^{38} - 32 q^{39} - 20 q^{40} - 12 q^{41} - 16 q^{42} + 4 q^{43} + 4 q^{45} - 32 q^{46} - 80 q^{47} - 32 q^{48} - 392 q^{49} + 10 q^{50} - 24 q^{52} + 4 q^{53} + 56 q^{54} + 20 q^{55} + 16 q^{58} - 24 q^{59} - 80 q^{60} - 32 q^{61} + 64 q^{62} - 704 q^{64} + 32 q^{65} + 32 q^{66} - 20 q^{68} - 16 q^{69} + 40 q^{70} + 28 q^{71} - 52 q^{72} + 28 q^{75} + 12 q^{76} + 8 q^{77} - 44 q^{78} - 22 q^{80} + 352 q^{81} + 8 q^{82} - 72 q^{83} + 120 q^{84} + 12 q^{85} + 4 q^{86} - 40 q^{87} + 128 q^{90} + 32 q^{91} - 112 q^{92} + 80 q^{93} - 8 q^{95} - 44 q^{96} + 12 q^{99} + O(q^{100}) \)

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.