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Properties

Label 2800.2.be
Level $2800$
Weight $2$
Character orbit 2800.be
Rep. character $\chi_{2800}(699,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $568$
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.be (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 560 \)
Character field: \(\Q(i)\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 984 584 400
Cusp forms 936 568 368
Eisenstein series 48 16 32

Trace form

\( 568 q + 8 q^{4} + O(q^{10}) \) \( 568 q + 8 q^{4} - 8 q^{11} + 28 q^{14} - 8 q^{16} + 8 q^{21} + 8 q^{29} + 64 q^{36} + 16 q^{39} + 40 q^{44} - 24 q^{46} + 8 q^{49} + 16 q^{51} - 32 q^{56} + 116 q^{64} - 144 q^{71} - 68 q^{74} - 520 q^{81} - 44 q^{84} + 64 q^{86} + 56 q^{91} - 88 q^{99} + O(q^{100}) \)

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

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