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Properties

Label 2535.2.bg
Level $2535$
Weight $2$
Character orbit 2535.bg
Rep. character $\chi_{2535}(596,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $824$
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.bg (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 1568 824 744
Cusp forms 1344 824 520
Eisenstein series 224 0 224

Trace form

\( 824 q + 12 q^{6} - 12 q^{7} + O(q^{10}) \) \( 824 q + 12 q^{6} - 12 q^{7} + 4 q^{15} + 424 q^{16} + 40 q^{18} + 12 q^{19} + 36 q^{21} + 56 q^{24} - 24 q^{27} + 16 q^{28} + 48 q^{30} + 28 q^{31} + 8 q^{33} - 40 q^{34} - 12 q^{36} + 4 q^{37} - 104 q^{42} + 84 q^{43} - 8 q^{45} - 64 q^{46} - 104 q^{48} + 84 q^{49} - 32 q^{54} + 16 q^{55} - 36 q^{57} + 120 q^{58} + 16 q^{60} + 16 q^{61} + 8 q^{63} - 168 q^{66} - 64 q^{67} - 72 q^{69} - 24 q^{72} - 60 q^{73} + 8 q^{76} + 4 q^{81} - 120 q^{82} - 44 q^{84} + 48 q^{85} - 8 q^{87} + 144 q^{88} + 36 q^{93} - 24 q^{94} - 4 q^{96} - 4 q^{97} + 40 q^{99} + O(q^{100}) \)

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

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