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Properties

Label 2015.2.d
Level $2015$
Weight $2$
Character orbit 2015.d
Rep. character $\chi_{2015}(311,\cdot)$
Character field $\Q$
Dimension $140$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 2015 = 5 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2015.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 228 140 88
Cusp forms 220 140 80
Eisenstein series 8 0 8

Trace form

\( 140 q - 140 q^{4} + 148 q^{9} + O(q^{10}) \) \( 140 q - 140 q^{4} + 148 q^{9} - 4 q^{10} + 8 q^{14} + 140 q^{16} + 48 q^{22} - 140 q^{25} - 32 q^{26} - 24 q^{27} + 16 q^{29} - 32 q^{30} + 8 q^{35} - 100 q^{36} - 24 q^{38} + 20 q^{39} + 12 q^{40} - 136 q^{42} - 104 q^{48} - 108 q^{49} + 24 q^{51} + 56 q^{52} - 8 q^{55} + 56 q^{56} - 16 q^{61} - 16 q^{62} - 188 q^{64} - 4 q^{65} + 88 q^{66} + 40 q^{68} - 8 q^{69} - 40 q^{74} + 24 q^{77} + 96 q^{78} - 40 q^{79} + 164 q^{81} + 40 q^{82} + 48 q^{87} - 160 q^{88} + 52 q^{90} - 16 q^{91} + 72 q^{92} - 136 q^{94} - 40 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2015, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)