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Properties

Label 2535.2.bw
Level $2535$
Weight $2$
Character orbit 2535.bw
Rep. character $\chi_{2535}(16,\cdot)$
Character field $\Q(\zeta_{39})$
Dimension $2928$
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.bw (of order \(39\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{39})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 8832 2928 5904
Cusp forms 8640 2928 5712
Eisenstein series 192 0 192

Trace form

\( 2928 q - 2 q^{3} + 124 q^{4} + 2 q^{7} + 122 q^{9} + O(q^{10}) \) \( 2928 q - 2 q^{3} + 124 q^{4} + 2 q^{7} + 122 q^{9} - 4 q^{10} + 8 q^{11} + 8 q^{12} + 68 q^{13} - 24 q^{14} + 136 q^{16} + 4 q^{17} + 8 q^{20} - 12 q^{21} + 108 q^{22} + 12 q^{23} - 24 q^{24} - 244 q^{25} + 32 q^{26} + 4 q^{27} + 36 q^{28} - 4 q^{30} + 64 q^{31} + 240 q^{32} + 244 q^{34} + 4 q^{35} + 124 q^{36} - 8 q^{37} + 164 q^{38} - 4 q^{39} + 24 q^{40} - 32 q^{41} + 4 q^{42} - 2 q^{43} + 8 q^{44} - 8 q^{46} + 48 q^{47} + 8 q^{48} + 308 q^{49} - 16 q^{51} + 232 q^{52} + 16 q^{53} - 12 q^{55} + 32 q^{56} + 48 q^{57} + 112 q^{58} - 400 q^{59} + 10 q^{61} + 280 q^{62} + 2 q^{63} - 256 q^{64} - 4 q^{65} + 168 q^{66} + 98 q^{67} + 236 q^{68} - 16 q^{70} - 320 q^{71} - 52 q^{73} - 20 q^{74} - 2 q^{75} - 252 q^{76} - 24 q^{77} + 244 q^{78} - 36 q^{79} + 32 q^{80} + 122 q^{81} + 284 q^{82} + 8 q^{83} + 12 q^{84} + 48 q^{86} - 24 q^{87} + 8 q^{88} + 48 q^{89} + 8 q^{90} + 218 q^{91} - 152 q^{92} + 6 q^{93} + 280 q^{94} + 8 q^{95} + 56 q^{96} + 26 q^{97} + 72 q^{98} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{2}^{\mathrm{old}}(2535, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(845, [\chi])\)\(^{\oplus 2}\)