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Properties

Label 2200.2.bi
Level $2200$
Weight $2$
Character orbit 2200.bi
Rep. character $\chi_{2200}(1179,\cdot)$
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.bi (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

\( 1424 q - 5 q^{2} - q^{4} + 5 q^{6} - 5 q^{8} - 1404 q^{9} + O(q^{10}) \) \( 1424 q - 5 q^{2} - q^{4} + 5 q^{6} - 5 q^{8} - 1404 q^{9} - 10 q^{10} - 6 q^{11} + 10 q^{12} - 9 q^{14} + 3 q^{16} - 10 q^{17} + 15 q^{18} - 10 q^{19} - q^{20} + 40 q^{22} - 10 q^{24} - 6 q^{25} + q^{26} - 5 q^{28} + 10 q^{30} - 50 q^{32} + 20 q^{33} - 8 q^{34} - 10 q^{35} - 2 q^{36} - 5 q^{38} - 5 q^{40} - 10 q^{41} - 5 q^{42} + 19 q^{44} - 5 q^{46} + 10 q^{48} + 320 q^{49} - 40 q^{50} + 10 q^{51} + 35 q^{52} + 5 q^{54} + q^{56} - 40 q^{58} - 2 q^{59} + 101 q^{60} - 80 q^{62} - 37 q^{64} + 50 q^{65} + 61 q^{66} - 20 q^{67} + 75 q^{68} + 3 q^{70} - 30 q^{72} - 10 q^{73} + 55 q^{74} - 6 q^{75} + 35 q^{78} - 61 q^{80} + 1320 q^{81} + 60 q^{82} - 10 q^{83} - 10 q^{84} + 17 q^{86} - 60 q^{88} - 12 q^{89} - 115 q^{90} + 12 q^{91} - 50 q^{94} - 10 q^{97} + 10 q^{98} - 52 q^{99} + O(q^{100}) \)

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.