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Properties

Label 2535.2.i
Level $2535$
Weight $2$
Character orbit 2535.i
Rep. character $\chi_{2535}(991,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $204$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 784 204 580
Cusp forms 672 204 468
Eisenstein series 112 0 112

Trace form

\( 204 q - 2 q^{3} - 100 q^{4} + 2 q^{7} - 102 q^{9} + O(q^{10}) \) \( 204 q - 2 q^{3} - 100 q^{4} + 2 q^{7} - 102 q^{9} - 4 q^{10} + 8 q^{11} + 8 q^{12} + 8 q^{14} - 88 q^{16} - 12 q^{17} + 8 q^{20} - 12 q^{21} - 12 q^{22} + 12 q^{23} - 24 q^{24} + 204 q^{25} + 4 q^{27} + 36 q^{28} - 16 q^{29} - 4 q^{30} + 12 q^{31} - 20 q^{32} - 16 q^{34} + 4 q^{35} - 100 q^{36} - 8 q^{37} - 64 q^{38} + 24 q^{40} - 32 q^{41} + 4 q^{42} - 2 q^{43} + 8 q^{44} - 8 q^{46} + 48 q^{47} + 8 q^{48} - 96 q^{49} + 112 q^{53} - 20 q^{55} - 16 q^{56} + 48 q^{57} + 8 q^{58} + 16 q^{59} - 46 q^{61} - 44 q^{62} + 2 q^{63} + 288 q^{64} - 40 q^{66} - 6 q^{67} - 120 q^{68} - 8 q^{69} - 16 q^{70} - 8 q^{71} - 52 q^{73} - 68 q^{74} - 2 q^{75} + 8 q^{76} + 104 q^{77} + 12 q^{79} + 32 q^{80} - 102 q^{81} - 40 q^{82} + 8 q^{83} + 12 q^{84} + 48 q^{86} - 40 q^{87} - 40 q^{88} + 48 q^{89} + 8 q^{90} - 56 q^{92} + 6 q^{93} + 40 q^{94} + 8 q^{95} + 56 q^{96} + 26 q^{97} + 72 q^{98} - 16 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2535, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(845, [\chi])\)\(^{\oplus 2}\)