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Properties

Label 2015.2.cl
Level $2015$
Weight $2$
Character orbit 2015.cl
Rep. character $\chi_{2015}(98,\cdot)$
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.cl (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

\( 880 q - 4 q^{2} + 2 q^{3} - 432 q^{4} - 2 q^{5} - 4 q^{6} + O(q^{10}) \) \( 880 q - 4 q^{2} + 2 q^{3} - 432 q^{4} - 2 q^{5} - 4 q^{6} - 8 q^{10} - 4 q^{11} - 14 q^{12} - 2 q^{13} + 24 q^{14} - 20 q^{15} - 424 q^{16} + 24 q^{18} + 8 q^{19} + 30 q^{20} - 12 q^{21} - 8 q^{22} - 8 q^{23} + 4 q^{24} + 8 q^{25} - 4 q^{26} - 28 q^{27} + 6 q^{28} - 8 q^{30} - 24 q^{31} - 14 q^{32} - 4 q^{33} + 16 q^{34} + 14 q^{35} - 6 q^{37} - 68 q^{38} - 16 q^{39} - 8 q^{40} - 12 q^{41} - 52 q^{42} + 8 q^{43} + 10 q^{45} - 32 q^{46} + 4 q^{48} - 784 q^{49} + 44 q^{50} + 24 q^{51} - 8 q^{52} + 4 q^{53} - 8 q^{54} - 10 q^{55} + 48 q^{57} - 12 q^{58} + 24 q^{59} + 42 q^{60} - 8 q^{61} - 58 q^{62} + 44 q^{63} + 800 q^{64} - 8 q^{65} - 16 q^{66} - 20 q^{67} - 2 q^{68} - 80 q^{69} - 90 q^{70} + 28 q^{71} - 102 q^{72} - 4 q^{73} - 28 q^{75} - 84 q^{76} + 4 q^{77} - 22 q^{78} + 192 q^{79} - 132 q^{80} + 364 q^{81} - 14 q^{82} + 18 q^{83} + 144 q^{84} - 8 q^{85} + 4 q^{86} - 76 q^{87} - 104 q^{90} + 56 q^{91} - 16 q^{92} + 30 q^{93} + 24 q^{94} - 16 q^{95} + 28 q^{96} + 32 q^{97} + 22 q^{98} - 12 q^{99} + O(q^{100}) \)

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.