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Properties

Label 2200.2.be
Level $2200$
Weight $2$
Character orbit 2200.be
Rep. character $\chi_{2200}(181,\cdot)$
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.be (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

\( 1424 q - q^{2} - q^{4} + q^{6} - 12 q^{7} - q^{8} - 1404 q^{9} + O(q^{10}) \) \( 1424 q - q^{2} - q^{4} + q^{6} - 12 q^{7} - q^{8} - 1404 q^{9} - 10 q^{10} + 8 q^{12} + 7 q^{14} + 12 q^{15} + 3 q^{16} - 2 q^{17} - 15 q^{18} - 21 q^{20} - 4 q^{22} - 12 q^{23} + 12 q^{24} - 6 q^{25} + q^{26} + 15 q^{28} + 8 q^{30} - 2 q^{31} - 46 q^{32} + 12 q^{33} - 8 q^{34} - 2 q^{36} - 51 q^{38} + 152 q^{39} - 25 q^{40} - 2 q^{41} + 3 q^{42} + 3 q^{44} + 7 q^{46} - 12 q^{47} + 2 q^{48} - 344 q^{49} + 32 q^{50} - q^{52} + 3 q^{54} + 48 q^{55} - 13 q^{56} + 24 q^{57} - 26 q^{58} + q^{60} + 2 q^{62} + 20 q^{63} + 35 q^{64} + 14 q^{65} + 85 q^{66} + 29 q^{68} - 23 q^{70} - 2 q^{71} + 54 q^{72} - 2 q^{73} - 15 q^{74} + 38 q^{76} + 15 q^{78} + 38 q^{79} + 35 q^{80} + 1320 q^{81} - 14 q^{82} - 6 q^{84} - 19 q^{86} + 24 q^{87} - 20 q^{88} - 12 q^{89} - 69 q^{90} + 46 q^{92} - 74 q^{94} + 34 q^{95} + 126 q^{96} + 30 q^{97} + 8 q^{98} + O(q^{100}) \)

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.