Properties

Label 2015.2.br
Level $2015$
Weight $2$
Character orbit 2015.br
Rep. character $\chi_{2015}(621,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $280$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 2015 = 5 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2015.br (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 456 280 176
Cusp forms 440 280 160
Eisenstein series 16 0 16

Trace form

\( 280 q + 140 q^{4} - 136 q^{9} + O(q^{10}) \) \( 280 q + 140 q^{4} - 136 q^{9} + 4 q^{10} + 12 q^{11} - 8 q^{14} + 12 q^{15} - 140 q^{16} - 12 q^{19} + 24 q^{22} - 48 q^{24} - 280 q^{25} - 16 q^{26} + 24 q^{27} + 12 q^{28} + 8 q^{29} - 16 q^{30} - 36 q^{33} - 20 q^{35} + 100 q^{36} + 72 q^{38} - 32 q^{39} + 24 q^{40} - 12 q^{41} - 8 q^{42} + 60 q^{46} + 8 q^{48} + 144 q^{49} - 24 q^{51} + 40 q^{52} + 72 q^{54} + 8 q^{55} - 32 q^{56} - 96 q^{58} + 12 q^{59} + 4 q^{61} + 16 q^{62} + 48 q^{63} - 376 q^{64} + 16 q^{65} - 112 q^{66} - 40 q^{68} + 20 q^{69} + 24 q^{71} - 20 q^{74} + 60 q^{76} - 24 q^{77} + 120 q^{78} - 32 q^{79} + 48 q^{80} - 140 q^{81} + 20 q^{82} - 12 q^{84} - 36 q^{85} - 24 q^{87} + 16 q^{88} - 48 q^{89} - 112 q^{90} + 28 q^{91} - 192 q^{92} - 44 q^{94} + 28 q^{95} + 12 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2015, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(403, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)