↑

Properties

Label 2015.2.fi
Level $2015$
Weight $2$
Character orbit 2015.fi
Rep. character $\chi_{2015}(289,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1760$
Sturm bound $448$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2015 = 5 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2015.fi (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

\( 1760 q - 222 q^{4} - 8 q^{5} + 418 q^{9} + O(q^{10}) \) \( 1760 q - 222 q^{4} - 8 q^{5} + 418 q^{9} - 24 q^{10} - 12 q^{11} - 40 q^{14} - 30 q^{15} + 190 q^{16} - 8 q^{19} - 67 q^{20} - 72 q^{21} + 22 q^{24} - 4 q^{25} - 18 q^{26} - 26 q^{29} + 8 q^{30} - 48 q^{31} - 8 q^{34} + 34 q^{35} - 784 q^{36} - 30 q^{39} - 85 q^{40} - 2 q^{41} - 16 q^{44} - 29 q^{45} - 14 q^{46} - 204 q^{49} + 6 q^{50} + 74 q^{51} + 124 q^{54} + 15 q^{55} - 42 q^{56} - 8 q^{59} - 94 q^{60} - 104 q^{61} + 288 q^{64} - 9 q^{65} - 84 q^{66} - 26 q^{69} + 114 q^{70} - 166 q^{71} + 12 q^{74} + 101 q^{75} - 64 q^{76} + 115 q^{80} - 394 q^{81} + 74 q^{84} + 15 q^{85} + 48 q^{86} - 6 q^{89} - 55 q^{90} + 16 q^{91} - 20 q^{94} - 89 q^{95} - 198 q^{96} + 6 q^{99} + O(q^{100}) \)

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.