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Properties

Label 2800.2.fr
Level $2800$
Weight $2$
Character orbit 2800.fr
Rep. character $\chi_{2800}(131,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $7616$
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.fr (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2800 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 7744 7744 0
Cusp forms 7616 7616 0
Eisenstein series 128 128 0

Trace form

\( 7616 q - 6 q^{2} - 18 q^{3} - 6 q^{4} - 24 q^{5} - 64 q^{7} + 12 q^{8} + O(q^{10}) \) \( 7616 q - 6 q^{2} - 18 q^{3} - 6 q^{4} - 24 q^{5} - 64 q^{7} + 12 q^{8} - 6 q^{10} - 6 q^{11} - 18 q^{12} - 6 q^{16} - 36 q^{17} - 18 q^{19} - 30 q^{21} - 24 q^{22} - 12 q^{23} - 48 q^{24} - 48 q^{26} + 12 q^{28} - 24 q^{29} + 8 q^{30} - 16 q^{32} - 36 q^{33} - 68 q^{35} + 128 q^{36} - 6 q^{37} - 18 q^{38} - 12 q^{39} + 36 q^{40} + 20 q^{42} - 64 q^{43} - 6 q^{44} - 42 q^{45} - 22 q^{46} - 64 q^{49} - 12 q^{50} + 8 q^{51} + 144 q^{52} - 6 q^{53} + 54 q^{54} - 96 q^{56} - 38 q^{58} - 18 q^{59} + 40 q^{60} - 18 q^{61} + 12 q^{64} - 16 q^{65} - 18 q^{66} - 42 q^{67} - 48 q^{68} + 6 q^{70} - 48 q^{71} - 38 q^{72} - 60 q^{74} - 24 q^{75} + 30 q^{77} - 96 q^{78} - 42 q^{80} - 900 q^{81} - 144 q^{82} + 22 q^{84} - 12 q^{85} + 34 q^{86} - 36 q^{87} + 60 q^{88} + 72 q^{91} + 52 q^{92} - 40 q^{93} - 18 q^{94} - 198 q^{96} + 56 q^{98} + 32 q^{99} + O(q^{100}) \)

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.