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Properties

Label 2200.2.fa
Level $2200$
Weight $2$
Character orbit 2200.fa
Rep. character $\chi_{2200}(203,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $2848$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 2200 = 2^{3} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2200.fa (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2200 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2200, [\chi])\).

Total New Old
Modular forms 2912 2912 0
Cusp forms 2848 2848 0
Eisenstein series 64 64 0

Trace form

\( 2848 q - 6 q^{2} - 12 q^{3} - 2 q^{6} - 6 q^{8} - 20 q^{9} + O(q^{10}) \) \( 2848 q - 6 q^{2} - 12 q^{3} - 2 q^{6} - 6 q^{8} - 20 q^{9} - 12 q^{11} + 26 q^{12} - 10 q^{14} - 12 q^{16} - 12 q^{17} - 32 q^{18} - 50 q^{20} - 42 q^{22} - 12 q^{25} - 12 q^{26} - 36 q^{27} - 70 q^{28} - 10 q^{30} - 46 q^{32} - 4 q^{33} - 20 q^{34} - 12 q^{35} + 6 q^{36} + 34 q^{38} - 10 q^{40} - 4 q^{41} - 50 q^{42} - 96 q^{43} + 30 q^{44} - 2 q^{46} - 24 q^{48} + 14 q^{50} - 24 q^{51} - 14 q^{52} + 40 q^{54} - 12 q^{56} + 84 q^{57} - 14 q^{58} - 20 q^{59} - 130 q^{60} - 54 q^{62} - 32 q^{65} + 18 q^{66} - 32 q^{67} + 90 q^{68} + 14 q^{70} + 10 q^{72} - 12 q^{73} - 110 q^{74} - 12 q^{75} + 16 q^{76} - 64 q^{78} + 184 q^{80} + 644 q^{81} + 46 q^{82} - 132 q^{83} - 10 q^{84} - 12 q^{86} - 2 q^{88} - 40 q^{89} + 70 q^{90} - 4 q^{91} + 84 q^{92} - 170 q^{94} - 2 q^{96} - 44 q^{97} - 96 q^{98} - 180 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2200, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.