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Properties

Label 2805.2.fa
Level $2805$
Weight $2$
Character orbit 2805.fa
Rep. character $\chi_{2805}(37,\cdot)$
Character field $\Q(\zeta_{80})$
Dimension $6912$
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.fa (of order \(80\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 935 \)
Character field: \(\Q(\zeta_{80})\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 14080 6912 7168
Cusp forms 13568 6912 6656
Eisenstein series 512 0 512

Trace form

\( 6912 q + O(q^{10}) \) \( 6912 q - 64 q^{14} + 32 q^{25} + 64 q^{26} + 128 q^{28} + 64 q^{31} - 16 q^{33} - 64 q^{34} + 64 q^{37} + 336 q^{40} - 192 q^{52} - 256 q^{55} - 96 q^{57} + 224 q^{58} - 128 q^{67} + 352 q^{68} - 64 q^{70} - 32 q^{73} - 64 q^{75} + 96 q^{77} + 64 q^{79} + 1008 q^{80} + 128 q^{83} + 192 q^{84} + 112 q^{85} - 128 q^{86} + 80 q^{88} - 480 q^{92} + 288 q^{93} + 128 q^{95} - 64 q^{97} + O(q^{100}) \)

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

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