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Properties

Label 2015.2.fm
Level $2015$
Weight $2$
Character orbit 2015.fm
Rep. character $\chi_{2015}(4,\cdot)$
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.fm (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

\( 1760 q + 210 q^{4} - 48 q^{6} - 218 q^{9} + O(q^{10}) \) \( 1760 q + 210 q^{4} - 48 q^{6} - 218 q^{9} - 9 q^{10} - 18 q^{11} - 24 q^{14} - 36 q^{15} + 202 q^{16} + 6 q^{19} + 27 q^{20} - 6 q^{24} - 24 q^{25} + 8 q^{26} + 10 q^{29} + 60 q^{30} - 32 q^{35} + 748 q^{36} - 28 q^{39} - 76 q^{40} + 30 q^{41} + 6 q^{45} - 54 q^{46} + 182 q^{49} + 108 q^{50} - 120 q^{51} + 66 q^{54} + 18 q^{55} + 124 q^{56} + 42 q^{59} + 96 q^{61} - 384 q^{64} + 9 q^{65} - 32 q^{66} + 34 q^{69} - 18 q^{71} + 74 q^{74} - 33 q^{75} + 12 q^{76} - 16 q^{79} + 72 q^{80} + 162 q^{81} - 354 q^{84} - 18 q^{85} - 18 q^{89} - 134 q^{90} + 6 q^{91} - 44 q^{95} + O(q^{100}) \)

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.