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Properties

Label 2535.2.b
Level $2535$
Weight $2$
Character orbit 2535.b
Rep. character $\chi_{2535}(1351,\cdot)$
Character field $\Q$
Dimension $104$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 392 104 288
Cusp forms 336 104 232
Eisenstein series 56 0 56

Trace form

\( 104 q - 4 q^{3} - 108 q^{4} + 104 q^{9} + O(q^{10}) \) \( 104 q - 4 q^{3} - 108 q^{4} + 104 q^{9} + 4 q^{10} + 12 q^{12} + 24 q^{14} + 100 q^{16} - 8 q^{17} - 16 q^{22} + 8 q^{23} - 104 q^{25} - 4 q^{27} + 16 q^{29} + 4 q^{30} + 8 q^{35} - 108 q^{36} - 32 q^{38} - 12 q^{40} + 16 q^{42} + 16 q^{43} + 4 q^{48} - 128 q^{49} + 8 q^{51} + 40 q^{53} - 16 q^{55} - 80 q^{56} + 48 q^{61} - 24 q^{62} - 124 q^{64} - 24 q^{66} + 24 q^{68} - 8 q^{69} - 16 q^{74} + 4 q^{75} - 88 q^{77} + 40 q^{79} + 104 q^{81} - 48 q^{82} - 8 q^{87} + 56 q^{88} + 4 q^{90} + 104 q^{92} + 16 q^{94} + 16 q^{95} + O(q^{100}) \)

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

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