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Properties

Label 2200.2.di
Level $2200$
Weight $2$
Character orbit 2200.di
Rep. character $\chi_{2200}(581,\cdot)$
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.di (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

\( 1424 q - 6 q^{2} - 6 q^{4} + q^{6} - 12 q^{7} - 6 q^{8} + 346 q^{9} + O(q^{10}) \) \( 1424 q - 6 q^{2} - 6 q^{4} + q^{6} - 12 q^{7} - 6 q^{8} + 346 q^{9} - 10 q^{10} + 8 q^{12} - 3 q^{14} - 18 q^{15} + 18 q^{16} - 2 q^{17} - 15 q^{18} - q^{20} + 11 q^{22} - 12 q^{23} + 12 q^{24} - 6 q^{25} + q^{26} - 25 q^{28} - 17 q^{30} - 2 q^{31} - 46 q^{32} - 18 q^{33} - 8 q^{34} - 17 q^{36} + 34 q^{38} - 58 q^{39} - 2 q^{41} + 13 q^{42} + 23 q^{44} - 13 q^{46} - 2 q^{47} + 2 q^{48} - 344 q^{49} + 22 q^{50} + 19 q^{52} + 3 q^{54} - 2 q^{55} - 13 q^{56} + 24 q^{57} - 46 q^{58} - 44 q^{60} - 68 q^{62} + 30 q^{63} - 30 q^{64} + 14 q^{65} - 80 q^{66} + 29 q^{68} + 27 q^{70} - 2 q^{71} - 36 q^{72} - 2 q^{73} - 15 q^{74} + 38 q^{76} + 15 q^{78} + 38 q^{79} - 10 q^{80} - 350 q^{81} - 14 q^{82} + 4 q^{84} - 14 q^{86} + 24 q^{87} + 75 q^{88} - 12 q^{89} - 39 q^{90} - 134 q^{92} + 41 q^{94} + 84 q^{95} - 74 q^{96} - 10 q^{97} + 8 q^{98} + O(q^{100}) \)

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.