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Properties

Label 2200.2.el
Level $2200$
Weight $2$
Character orbit 2200.el
Rep. character $\chi_{2200}(491,\cdot)$
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.el (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

\( 1424 q - 5 q^{2} - 12 q^{3} - q^{4} - 15 q^{6} - 5 q^{8} + 1380 q^{9} + O(q^{10}) \) \( 1424 q - 5 q^{2} - 12 q^{3} - q^{4} - 15 q^{6} - 5 q^{8} + 1380 q^{9} + 10 q^{10} - 6 q^{11} - 20 q^{12} + 7 q^{14} - 5 q^{16} - 10 q^{17} - 25 q^{18} - 10 q^{19} - q^{20} + 20 q^{22} - 10 q^{24} - 6 q^{25} - 13 q^{26} - 48 q^{27} - 5 q^{28} - 20 q^{30} - 24 q^{33} - 4 q^{34} - 10 q^{35} - 8 q^{36} + 33 q^{38} - 5 q^{40} - 10 q^{41} - 17 q^{42} + 19 q^{44} - 5 q^{46} - 4 q^{48} - 344 q^{49} + 30 q^{50} - 50 q^{51} - 45 q^{52} - 65 q^{54} - 13 q^{56} - 20 q^{57} - 10 q^{58} - 2 q^{59} - 33 q^{60} + 70 q^{62} - 37 q^{64} - 50 q^{65} - 31 q^{66} - 12 q^{67} + 25 q^{68} + 21 q^{70} - 60 q^{72} - 10 q^{73} + 35 q^{74} - 6 q^{75} - 3 q^{78} - 45 q^{80} + 1248 q^{81} + 2 q^{82} - 10 q^{83} - 19 q^{86} - 20 q^{88} - 12 q^{89} - 115 q^{90} - 16 q^{91} + 94 q^{92} - 30 q^{94} - 34 q^{97} - 10 q^{98} - 88 q^{99} + O(q^{100}) \)

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.