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Properties

Label 2200.2.bs
Level $2200$
Weight $2$
Character orbit 2200.bs
Rep. character $\chi_{2200}(211,\cdot)$
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.bs (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

\( 1424 q - 5 q^{2} - 2 q^{3} - q^{4} - 5 q^{6} - 5 q^{8} - 350 q^{9} + O(q^{10}) \) \( 1424 q - 5 q^{2} - 2 q^{3} - q^{4} - 5 q^{6} - 5 q^{8} - 350 q^{9} + 20 q^{10} - 6 q^{11} + 10 q^{12} - 3 q^{14} - 5 q^{16} - 10 q^{17} + 5 q^{18} - 10 q^{19} - 6 q^{20} - 25 q^{22} - 10 q^{24} - 6 q^{25} - 18 q^{26} - 8 q^{27} + 5 q^{30} + 6 q^{33} - 4 q^{34} - 10 q^{35} + 12 q^{36} - 27 q^{38} - 40 q^{40} + 38 q^{42} - q^{44} - 5 q^{46} - 24 q^{48} - 344 q^{49} + 30 q^{50} + 10 q^{51} - 25 q^{52} - 30 q^{54} + 22 q^{56} - 20 q^{57} - 20 q^{58} - 2 q^{59} + 42 q^{60} + 95 q^{62} - 37 q^{64} - 21 q^{66} - 12 q^{67} - 45 q^{68} - 59 q^{70} - 55 q^{74} - 26 q^{75} + 32 q^{78} + 80 q^{80} - 332 q^{81} - 48 q^{82} - 10 q^{83} + 60 q^{84} - 19 q^{86} + 35 q^{88} - 12 q^{89} + 90 q^{90} + 44 q^{91} - 146 q^{92} + 40 q^{94} + 105 q^{96} + 6 q^{97} - 105 q^{98} + 32 q^{99} + O(q^{100}) \)

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.