Properties

Label 2200.2.do
Level $2200$
Weight $2$
Character orbit 2200.do
Rep. character $\chi_{2200}(141,\cdot)$
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.do (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

\( 1424 q - q^{2} - q^{4} + 6 q^{6} - 12 q^{7} - q^{8} + 346 q^{9} + O(q^{10}) \) \( 1424 q - q^{2} - q^{4} + 6 q^{6} - 12 q^{7} - q^{8} + 346 q^{9} - 22 q^{12} + 2 q^{14} - 18 q^{15} + 3 q^{16} - 12 q^{17} + 5 q^{18} - 21 q^{20} - 29 q^{22} - 12 q^{23} - 18 q^{24} - 6 q^{25} + 6 q^{26} + 15 q^{28} + 23 q^{30} - 2 q^{31} + 4 q^{32} + 12 q^{33} - 8 q^{34} - 42 q^{36} - 41 q^{38} - 28 q^{39} + 40 q^{40} - 2 q^{41} + 13 q^{42} - 32 q^{44} + 2 q^{46} - 2 q^{47} - 13 q^{48} - 344 q^{49} + 22 q^{50} + 34 q^{52} - 32 q^{54} - 82 q^{55} + 22 q^{56} - 36 q^{57} + 9 q^{58} - 14 q^{60} - 78 q^{62} - 40 q^{63} - 25 q^{64} - 36 q^{65} + 35 q^{66} - 41 q^{68} - 83 q^{70} - 2 q^{71} + 19 q^{72} - 2 q^{73} - 15 q^{74} - 52 q^{76} + 20 q^{78} - 172 q^{79} + 70 q^{80} - 320 q^{81} + 36 q^{82} - 76 q^{84} + 31 q^{86} - 36 q^{87} + 75 q^{88} - 12 q^{89} + q^{90} + 51 q^{92} - 54 q^{94} + 84 q^{95} + 21 q^{96} + 20 q^{97} + 53 q^{98} + O(q^{100}) \)

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

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