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Properties

Label 2800.2.df
Level $2800$
Weight $2$
Character orbit 2800.df
Rep. character $\chi_{2800}(501,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1192$
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.df (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
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 1240 728
Cusp forms 1872 1192 680
Eisenstein series 96 48 48

Trace form

\( 1192 q + 2 q^{2} + 2 q^{3} - 24 q^{6} + 20 q^{8} + O(q^{10}) \) \( 1192 q + 2 q^{2} + 2 q^{3} - 24 q^{6} + 20 q^{8} - 10 q^{11} + 2 q^{12} + 8 q^{13} + 8 q^{14} + 4 q^{16} + 4 q^{17} + 30 q^{18} + 2 q^{19} - 6 q^{21} - 20 q^{22} + 22 q^{24} - 6 q^{26} + 20 q^{27} + 10 q^{28} + 24 q^{29} - 36 q^{31} + 12 q^{32} + 4 q^{33} + 64 q^{34} - 32 q^{36} - 6 q^{37} + 22 q^{38} + 30 q^{42} - 26 q^{44} + 12 q^{46} - 36 q^{47} + 120 q^{48} + 8 q^{49} + 2 q^{51} - 28 q^{52} + 10 q^{53} + 6 q^{54} + 8 q^{56} + 22 q^{58} + 18 q^{59} - 6 q^{61} - 116 q^{62} + 36 q^{63} + 30 q^{66} + 10 q^{67} - 4 q^{68} - 28 q^{69} - 52 q^{72} + 22 q^{74} + 36 q^{76} + 18 q^{77} - 84 q^{78} + 4 q^{79} + 488 q^{81} + 18 q^{82} + 48 q^{83} - 84 q^{84} - 24 q^{86} + 14 q^{88} + 44 q^{92} - 10 q^{93} - 34 q^{94} + 52 q^{96} + 16 q^{97} + 4 q^{98} + 120 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)