Properties

Label 2805.2.ec
Level $2805$
Weight $2$
Character orbit 2805.ec
Rep. character $\chi_{2805}(217,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1728$
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.ec (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 935 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 3520 1728 1792
Cusp forms 3392 1728 1664
Eisenstein series 128 0 128

Trace form

\( 1728 q - 8 q^{5} + 40 q^{7} - 432 q^{9} + O(q^{10}) \) \( 1728 q - 8 q^{5} + 40 q^{7} - 432 q^{9} + 16 q^{14} - 8 q^{15} + 432 q^{16} - 20 q^{17} + 32 q^{20} + 12 q^{25} + 16 q^{31} - 4 q^{33} + 140 q^{40} - 8 q^{45} - 40 q^{46} + 432 q^{49} + 80 q^{52} - 16 q^{55} - 64 q^{56} + 80 q^{57} + 64 q^{59} - 40 q^{61} - 40 q^{63} + 80 q^{68} + 32 q^{71} + 32 q^{75} + 8 q^{77} - 40 q^{79} - 84 q^{80} - 432 q^{81} + 80 q^{85} - 136 q^{88} - 48 q^{91} - 80 q^{92} - 20 q^{95} + O(q^{100}) \)

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

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