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Properties

Label 2015.2.fu
Level $2015$
Weight $2$
Character orbit 2015.fu
Rep. character $\chi_{2015}(51,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1184$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 2015 = 5 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2015.fu (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 403 \)
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 1184 640
Cusp forms 1760 1184 576
Eisenstein series 64 0 64

Trace form

\( 1184 q - 4 q^{3} + 288 q^{4} + 144 q^{9} + O(q^{10}) \) \( 1184 q - 4 q^{3} + 288 q^{4} + 144 q^{9} + 44 q^{12} - 4 q^{13} - 8 q^{14} - 288 q^{16} + 24 q^{17} - 12 q^{22} - 104 q^{23} + 592 q^{25} + 28 q^{26} - 16 q^{27} + 8 q^{29} + 64 q^{30} + 500 q^{36} - 48 q^{38} - 34 q^{39} - 160 q^{43} - 76 q^{48} - 124 q^{49} - 8 q^{51} + 100 q^{52} + 32 q^{55} - 28 q^{56} + 40 q^{61} - 8 q^{62} + 92 q^{64} + 112 q^{66} + 272 q^{68} + 480 q^{69} - 200 q^{74} + 4 q^{75} - 304 q^{77} + 32 q^{78} - 100 q^{79} - 28 q^{81} - 40 q^{82} - 132 q^{87} - 184 q^{88} + 48 q^{90} - 58 q^{91} - 376 q^{92} + 40 q^{94} + 16 q^{95} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(2015, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2015, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(403, [\chi])\)\(^{\oplus 2}\)