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Properties

Label 2200.2.g
Level $2200$
Weight $2$
Character orbit 2200.g
Rep. character $\chi_{2200}(1101,\cdot)$
Character field $\Q$
Dimension $190$
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.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2200, [\chi])\).

Total New Old
Modular forms 372 190 182
Cusp forms 348 190 158
Eisenstein series 24 0 24

Trace form

\( 190 q + 4 q^{4} + 10 q^{6} - 12 q^{8} - 190 q^{9} + O(q^{10}) \) \( 190 q + 4 q^{4} + 10 q^{6} - 12 q^{8} - 190 q^{9} - 4 q^{12} - 8 q^{14} + 4 q^{17} + 18 q^{18} - 12 q^{23} + 20 q^{24} - 12 q^{26} + 32 q^{28} + 4 q^{31} + 20 q^{32} - 40 q^{36} - 8 q^{38} + 24 q^{39} - 4 q^{41} + 20 q^{42} - 4 q^{44} + 18 q^{46} + 44 q^{47} - 24 q^{48} + 174 q^{49} - 16 q^{52} - 18 q^{54} + 36 q^{56} + 16 q^{57} + 28 q^{58} - 14 q^{62} - 40 q^{63} + 28 q^{64} + 10 q^{66} + 24 q^{68} + 12 q^{71} + 96 q^{72} + 36 q^{73} + 46 q^{74} - 72 q^{76} - 56 q^{78} - 16 q^{79} + 206 q^{81} - 4 q^{82} - 24 q^{84} - 8 q^{86} - 80 q^{87} + 12 q^{88} + 4 q^{89} - 52 q^{92} + 8 q^{94} - 84 q^{96} - 12 q^{97} + 88 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(2200, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)