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Properties

Label 2800.2.t
Level $2800$
Weight $2$
Character orbit 2800.t
Rep. character $\chi_{2800}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $432$
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.t (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
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 984 432 552
Cusp forms 936 432 504
Eisenstein series 48 0 48

Trace form

\( 432 q - 16 q^{4} - 432 q^{9} + O(q^{10}) \) \( 432 q - 16 q^{4} - 432 q^{9} + 16 q^{12} - 16 q^{16} + 28 q^{18} + 32 q^{19} - 4 q^{22} - 64 q^{26} - 64 q^{34} + 64 q^{36} + 56 q^{38} + 20 q^{42} - 64 q^{43} + 52 q^{44} + 64 q^{46} + 80 q^{48} + 32 q^{51} + 16 q^{52} - 64 q^{54} - 12 q^{56} - 52 q^{58} + 64 q^{61} + 40 q^{62} - 64 q^{64} - 64 q^{66} + 24 q^{68} + 64 q^{69} - 80 q^{72} + 16 q^{73} + 64 q^{74} - 76 q^{78} + 432 q^{81} - 56 q^{82} - 64 q^{86} + 112 q^{87} - 88 q^{88} + 136 q^{92} + 16 q^{94} - 64 q^{96} - 128 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)