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Properties

Label 2535.2.bb
Level $2535$
Weight $2$
Character orbit 2535.bb
Rep. character $\chi_{2535}(316,\cdot)$
Character field $\Q(\zeta_{6})$
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.bb (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 204 q + 2 q^{3} + 100 q^{4} - 6 q^{7} - 102 q^{9} + O(q^{10}) \) \( 204 q + 2 q^{3} + 100 q^{4} - 6 q^{7} - 102 q^{9} - 4 q^{10} + 8 q^{12} + 24 q^{14} - 104 q^{16} + 20 q^{17} + 12 q^{19} + 24 q^{20} - 20 q^{22} + 4 q^{23} - 204 q^{25} - 4 q^{27} + 12 q^{28} - 16 q^{29} - 4 q^{30} - 60 q^{32} + 4 q^{35} + 100 q^{36} + 12 q^{37} - 16 q^{38} - 24 q^{40} + 20 q^{42} - 18 q^{43} - 72 q^{46} + 24 q^{48} + 124 q^{49} - 32 q^{51} + 80 q^{53} + 4 q^{55} + 8 q^{56} + 24 q^{58} - 58 q^{61} + 84 q^{62} + 6 q^{63} - 256 q^{64} + 24 q^{66} + 30 q^{67} - 72 q^{68} + 8 q^{69} - 48 q^{71} - 20 q^{74} - 2 q^{75} + 48 q^{76} - 104 q^{77} + 4 q^{79} - 102 q^{81} + 48 q^{82} - 36 q^{84} + 8 q^{87} + 16 q^{88} - 24 q^{89} + 8 q^{90} + 40 q^{92} + 6 q^{93} - 40 q^{94} + 8 q^{95} + 18 q^{97} + 96 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2535, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(845, [\chi])\)\(^{\oplus 2}\)