Properties

Label 2535.2.bu
Level $2535$
Weight $2$
Character orbit 2535.bu
Rep. character $\chi_{2535}(79,\cdot)$
Character field $\Q(\zeta_{26})$
Dimension $2160$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 2535 = 3 \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2535.bu (of order \(26\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 845 \)
Character field: \(\Q(\zeta_{26})\)
Sturm bound: \(728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2535, [\chi])\).

Total New Old
Modular forms 4416 2160 2256
Cusp forms 4320 2160 2160
Eisenstein series 96 0 96

Trace form

\( 2160 q + 176 q^{4} + 4 q^{5} + 180 q^{9} + O(q^{10}) \) \( 2160 q + 176 q^{4} + 4 q^{5} + 180 q^{9} - 8 q^{11} + 24 q^{14} + 4 q^{15} - 184 q^{16} + 8 q^{19} - 28 q^{20} - 8 q^{21} - 8 q^{25} + 8 q^{29} + 36 q^{31} + 40 q^{34} - 12 q^{35} - 176 q^{36} + 8 q^{39} - 40 q^{40} + 8 q^{41} + 40 q^{44} - 4 q^{45} + 24 q^{46} + 40 q^{49} - 40 q^{50} + 16 q^{51} + 66 q^{55} - 184 q^{59} + 92 q^{60} + 136 q^{64} - 4 q^{65} + 8 q^{66} - 24 q^{69} + 152 q^{70} - 8 q^{71} + 128 q^{74} - 16 q^{75} + 140 q^{76} + 8 q^{79} + 20 q^{80} - 180 q^{81} + 32 q^{84} - 70 q^{85} - 312 q^{86} + 8 q^{89} - 12 q^{91} - 68 q^{94} + 172 q^{95} + 40 q^{96} + 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2535, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2535, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2535, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(845, [\chi])\)\(^{\oplus 2}\)