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Properties

Label 2015.2.ge
Level $2015$
Weight $2$
Character orbit 2015.ge
Rep. character $\chi_{2015}(189,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $3520$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 2015 = 5 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2015.ge (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2015 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 3648 3648 0
Cusp forms 3520 3520 0
Eisenstein series 128 128 0

Trace form

\( 3520 q - 36 q^{4} - 8 q^{5} - 24 q^{6} - 860 q^{9} + O(q^{10}) \) \( 3520 q - 36 q^{4} - 8 q^{5} - 24 q^{6} - 860 q^{9} - 24 q^{10} - 28 q^{11} - 88 q^{14} - 32 q^{15} - 428 q^{16} - 20 q^{19} - 14 q^{20} - 68 q^{21} + 112 q^{24} - 48 q^{26} - 44 q^{29} - 16 q^{31} - 100 q^{34} + 14 q^{35} + 24 q^{36} - 52 q^{39} - 28 q^{40} - 52 q^{41} - 12 q^{44} - 124 q^{45} - 72 q^{49} - 72 q^{50} + 96 q^{51} - 52 q^{54} - 10 q^{55} - 432 q^{56} - 52 q^{59} - 56 q^{60} - 102 q^{65} - 16 q^{66} + 36 q^{69} + 142 q^{70} + 124 q^{71} - 56 q^{74} + 36 q^{75} + 412 q^{76} - 64 q^{79} - 10 q^{80} - 772 q^{81} - 196 q^{84} - 182 q^{85} - 172 q^{86} - 40 q^{89} + 126 q^{90} + 16 q^{91} - 32 q^{94} + 42 q^{95} + 212 q^{96} + 108 q^{99} + O(q^{100}) \)

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.