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Properties

Label 2200.2.ch
Level $2200$
Weight $2$
Character orbit 2200.ch
Rep. character $\chi_{2200}(949,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $848$
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.ch (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 440 \)
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 1488 880 608
Cusp forms 1392 848 544
Eisenstein series 96 32 64

Trace form

\( 848 q + 6 q^{4} - 14 q^{6} - 192 q^{9} + O(q^{10}) \) \( 848 q + 6 q^{4} - 14 q^{6} - 192 q^{9} + 6 q^{14} + 26 q^{16} + 50 q^{24} - 68 q^{26} - 12 q^{31} + 40 q^{34} - 20 q^{36} + 68 q^{39} - 12 q^{41} - 38 q^{44} + 200 q^{49} + 196 q^{54} + 48 q^{56} - 54 q^{64} - 12 q^{66} - 44 q^{71} + 42 q^{74} - 4 q^{76} - 28 q^{79} - 216 q^{81} + 44 q^{84} - 34 q^{86} + 32 q^{89} + 56 q^{94} - 180 q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 2}\)