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Properties

Label 2805.2.bz
Level $2805$
Weight $2$
Character orbit 2805.bz
Rep. character $\chi_{2805}(529,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $704$
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.bz (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 85 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 1760 704 1056
Cusp forms 1696 704 992
Eisenstein series 64 0 64

Trace form

\( 704 q + 16 q^{6} + O(q^{10}) \) \( 704 q + 16 q^{6} - 16 q^{10} - 32 q^{14} - 608 q^{16} - 32 q^{19} - 80 q^{20} + 16 q^{24} + 64 q^{25} + 64 q^{26} + 128 q^{29} + 16 q^{34} + 64 q^{35} - 16 q^{36} + 64 q^{40} - 160 q^{41} + 32 q^{44} + 32 q^{45} - 64 q^{50} - 16 q^{54} - 32 q^{59} + 64 q^{61} + 128 q^{65} + 128 q^{69} - 32 q^{70} + 32 q^{71} - 224 q^{74} - 64 q^{76} - 128 q^{79} - 16 q^{85} + 64 q^{86} - 16 q^{90} + 128 q^{91} - 144 q^{94} - 64 q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2805, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(935, [\chi])\)\(^{\oplus 2}\)