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Properties

Label 2805.2.cn
Level $2805$
Weight $2$
Character orbit 2805.cn
Rep. character $\chi_{2805}(239,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $1536$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 2805 = 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2805.cn (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2805, [\chi])\).

Total New Old
Modular forms 1760 1536 224
Cusp forms 1696 1536 160
Eisenstein series 64 0 64

Trace form

\( 1536 q + 384 q^{4} - 4 q^{9} + O(q^{10}) \) \( 1536 q + 384 q^{4} - 4 q^{9} + 10 q^{15} - 336 q^{16} + 6 q^{25} - 60 q^{30} - 32 q^{36} - 60 q^{40} + 148 q^{45} - 432 q^{49} - 38 q^{55} - 28 q^{60} + 300 q^{64} + 156 q^{66} - 108 q^{69} + 20 q^{70} - 22 q^{75} + 108 q^{81} - 180 q^{90} - 64 q^{91} - 160 q^{94} + 20 q^{96} - 96 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2805, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(2805, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2805, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)