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

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

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

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