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Properties

Label 2800.2.dh
Level $2800$
Weight $2$
Character orbit 2800.dh
Rep. character $\chi_{2800}(149,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1136$
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.dh (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 560 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 1968 1168 800
Cusp forms 1872 1136 736
Eisenstein series 96 32 64

Trace form

\( 1136 q + 4 q^{4} - 16 q^{6} + O(q^{10}) \) \( 1136 q + 4 q^{4} - 16 q^{6} - 4 q^{11} - 16 q^{14} - 4 q^{16} + 4 q^{19} - 20 q^{21} + 4 q^{24} - 4 q^{26} + 16 q^{29} + 40 q^{31} + 64 q^{34} - 128 q^{36} + 20 q^{44} - 20 q^{46} + 16 q^{49} + 20 q^{51} + 36 q^{54} + 48 q^{56} - 28 q^{59} - 4 q^{61} + 64 q^{64} + 60 q^{66} + 40 q^{69} + 36 q^{74} - 136 q^{76} + 8 q^{79} + 496 q^{81} + 16 q^{84} - 60 q^{86} + 80 q^{91} - 12 q^{94} + 100 q^{96} + 64 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)