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Properties

Label 2200.2.cg
Level $2200$
Weight $2$
Character orbit 2200.cg
Rep. character $\chi_{2200}(389,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $1424$
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.cg (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2200 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 1456 1456 0
Cusp forms 1424 1424 0
Eisenstein series 32 32 0

Trace form

\( 1424 q - 6 q^{4} - 3 q^{6} - 350 q^{9} + O(q^{10}) \) \( 1424 q - 6 q^{4} - 3 q^{6} - 350 q^{9} - 22 q^{10} - 30 q^{12} + q^{14} + 6 q^{15} - 30 q^{16} - 10 q^{17} + 35 q^{18} - q^{20} - 5 q^{22} - 20 q^{23} - 24 q^{24} - 6 q^{25} - 13 q^{26} - 45 q^{28} + 7 q^{30} - 2 q^{31} - 10 q^{33} - 4 q^{34} + 7 q^{36} - 10 q^{39} - 2 q^{40} - 2 q^{41} - 15 q^{42} + 23 q^{44} + 11 q^{46} - 10 q^{47} + 10 q^{48} + 320 q^{49} - 8 q^{50} + 15 q^{52} - 27 q^{54} - 34 q^{55} + q^{56} + 60 q^{57} - 86 q^{60} - 10 q^{62} - 10 q^{63} - 30 q^{64} - 46 q^{65} + 50 q^{66} - 75 q^{68} - 53 q^{70} - 2 q^{71} + 110 q^{72} - 10 q^{73} - 19 q^{74} - 22 q^{76} - 55 q^{78} + 38 q^{79} + 14 q^{80} - 302 q^{81} + 60 q^{82} + 42 q^{84} + 2 q^{86} - 20 q^{87} - 45 q^{88} - 12 q^{89} + 77 q^{90} - 50 q^{92} + 45 q^{94} - 36 q^{95} + 72 q^{96} + 30 q^{97} + O(q^{100}) \)

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.