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Properties

Label 2200.2.cs
Level $2200$
Weight $2$
Character orbit 2200.cs
Rep. character $\chi_{2200}(131,\cdot)$
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.cs (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

\( 1424 q - 12 q^{3} - 6 q^{4} - 360 q^{9} + O(q^{10}) \) \( 1424 q - 12 q^{3} - 6 q^{4} - 360 q^{9} - 6 q^{11} - 10 q^{12} - 18 q^{14} - 30 q^{16} - 6 q^{20} - 16 q^{25} - 28 q^{26} + 12 q^{27} + 6 q^{33} - 14 q^{34} + 22 q^{36} - 42 q^{38} - 22 q^{42} - 16 q^{44} + 6 q^{48} + 1296 q^{49} - 48 q^{56} + 80 q^{58} - 12 q^{59} - 38 q^{60} + 18 q^{64} + 24 q^{66} - 12 q^{67} - 44 q^{70} - 36 q^{75} + 32 q^{78} - 50 q^{80} - 312 q^{81} - 108 q^{82} + 36 q^{86} - 20 q^{88} - 12 q^{89} - 96 q^{91} + 44 q^{92} + 36 q^{97} + 32 q^{99} + O(q^{100}) \)

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.