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Properties

Label 2800.2.eo
Level $2800$
Weight $2$
Character orbit 2800.eo
Rep. character $\chi_{2800}(547,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $2880$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 2800 = 2^{4} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2800.eo (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 400 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2800, [\chi])\).

Total New Old
Modular forms 3872 2880 992
Cusp forms 3808 2880 928
Eisenstein series 64 0 64

Trace form

\( 2880 q + 720 q^{9} + O(q^{10}) \) \( 2880 q + 720 q^{9} + 16 q^{12} - 80 q^{16} + 28 q^{18} + 96 q^{22} + 36 q^{30} + 56 q^{38} - 108 q^{40} + 20 q^{42} - 64 q^{43} + 140 q^{44} - 180 q^{48} - 92 q^{50} + 16 q^{52} + 68 q^{58} + 28 q^{60} + 40 q^{62} + 24 q^{68} - 80 q^{72} + 16 q^{73} + 88 q^{75} + 184 q^{78} - 128 q^{80} - 720 q^{81} + 24 q^{82} + 200 q^{86} + 112 q^{87} - 88 q^{88} - 88 q^{90} + 136 q^{92} + 320 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2800, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2800, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)