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Properties

Label 2015.2.fb
Level $2015$
Weight $2$
Character orbit 2015.fb
Rep. character $\chi_{2015}(9,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1760$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 2015 = 5 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2015.fb (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2015 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2015, [\chi])\).

Total New Old
Modular forms 1824 1824 0
Cusp forms 1760 1760 0
Eisenstein series 64 64 0

Trace form

\( 1760 q - 222 q^{4} - 8 q^{5} - 224 q^{9} + O(q^{10}) \) \( 1760 q - 222 q^{4} - 8 q^{5} - 224 q^{9} + 3 q^{10} - 6 q^{11} - 40 q^{14} + 15 q^{15} + 190 q^{16} - 14 q^{19} + 56 q^{20} - 72 q^{21} - 146 q^{24} - 4 q^{25} - 6 q^{26} - 26 q^{29} + 8 q^{30} - 48 q^{31} - 8 q^{34} - 41 q^{35} + 1568 q^{36} - 30 q^{39} - 85 q^{40} - 26 q^{41} - 16 q^{44} + 43 q^{45} + 46 q^{46} + 378 q^{49} - 63 q^{50} + 74 q^{51} - 236 q^{54} - 15 q^{55} + 84 q^{56} - 14 q^{59} - 94 q^{60} - 104 q^{61} + 288 q^{64} - 39 q^{65} - 84 q^{66} + 22 q^{69} + 114 q^{70} + 68 q^{71} + 66 q^{74} - 52 q^{75} + 212 q^{76} - 170 q^{80} + 182 q^{81} - 52 q^{84} + 48 q^{86} - 6 q^{89} - 55 q^{90} - 14 q^{91} - 20 q^{94} + 106 q^{95} - 198 q^{96} + 6 q^{99} + O(q^{100}) \)

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.