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Properties

Label 2535.2.bh
Level $2535$
Weight $2$
Character orbit 2535.bh
Rep. character $\chi_{2535}(89,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1152$
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.bh (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 195 \)
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 1312 256
Cusp forms 1344 1152 192
Eisenstein series 224 160 64

Trace form

\( 1152 q + 24 q^{4} + 4 q^{9} + O(q^{10}) \) \( 1152 q + 24 q^{4} + 4 q^{9} + 36 q^{10} - 10 q^{15} + 496 q^{16} + 16 q^{21} + 28 q^{24} - 18 q^{30} + 40 q^{31} + 32 q^{34} + 60 q^{36} - 184 q^{40} - 4 q^{45} + 128 q^{46} - 60 q^{54} - 44 q^{55} - 20 q^{60} + 40 q^{61} - 120 q^{66} - 72 q^{69} - 168 q^{70} - 66 q^{75} + 80 q^{76} - 96 q^{79} - 96 q^{81} + 132 q^{84} + 20 q^{85} - 184 q^{94} - 204 q^{96} + 48 q^{99} + O(q^{100}) \)

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

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