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Properties

Label 2800.2.r
Level $2800$
Weight $2$
Character orbit 2800.r
Rep. character $\chi_{2800}(293,\cdot)$
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.r (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

\( 568 q + 4 q^{2} - 8 q^{8} - 552 q^{9} + O(q^{10}) \) \( 568 q + 4 q^{2} - 8 q^{8} - 552 q^{9} - 8 q^{11} - 8 q^{16} - 4 q^{21} + 12 q^{22} + 32 q^{28} + 24 q^{32} - 40 q^{36} + 8 q^{37} + 48 q^{39} + 32 q^{42} + 12 q^{44} - 8 q^{46} - 8 q^{51} - 4 q^{56} - 24 q^{57} + 4 q^{58} + 32 q^{63} + 64 q^{72} - 128 q^{74} + 28 q^{78} + 488 q^{81} + 132 q^{84} - 40 q^{86} - 96 q^{88} + 28 q^{91} + 56 q^{92} - 16 q^{93} + 80 q^{98} + 24 q^{99} + O(q^{100}) \)

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

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