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Properties

Label 2800.2.bc
Level $2800$
Weight $2$
Character orbit 2800.bc
Rep. character $\chi_{2800}(251,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $596$
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.bc (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
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 984 620 364
Cusp forms 936 596 340
Eisenstein series 48 24 24

Trace form

\( 596 q + 4 q^{2} + 6 q^{4} + 4 q^{7} + 16 q^{8} + O(q^{10}) \) \( 596 q + 4 q^{2} + 6 q^{4} + 4 q^{7} + 16 q^{8} - 16 q^{11} - 18 q^{14} - 22 q^{16} - 14 q^{18} - 12 q^{21} + 30 q^{22} + 16 q^{23} - 12 q^{28} - 4 q^{29} - 16 q^{32} + 16 q^{36} - 4 q^{37} + 8 q^{39} - 20 q^{42} + 8 q^{43} + 34 q^{44} + 16 q^{46} + 4 q^{49} - 64 q^{51} - 4 q^{53} + 2 q^{56} + 10 q^{58} - 6 q^{64} + 8 q^{67} - 88 q^{71} - 10 q^{72} - 94 q^{74} + 16 q^{77} + 136 q^{78} - 524 q^{81} - 20 q^{84} - 46 q^{86} - 50 q^{88} + 20 q^{91} + 24 q^{92} + 16 q^{93} + 16 q^{98} + 24 q^{99} + O(q^{100}) \)

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

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