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Properties

Label 2200.2.t
Level $2200$
Weight $2$
Character orbit 2200.t
Rep. character $\chi_{2200}(1693,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $424$
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.t (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 440 \)
Character field: \(\Q(i)\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 744 440 304
Cusp forms 696 424 272
Eisenstein series 48 16 32

Trace form

\( 424 q + O(q^{10}) \) \( 424 q + 32 q^{12} - 24 q^{16} + 4 q^{22} + 8 q^{23} + 40 q^{26} - 16 q^{31} - 8 q^{33} + 88 q^{36} - 32 q^{38} + 8 q^{47} - 8 q^{48} + 96 q^{56} + 12 q^{66} - 80 q^{71} - 376 q^{81} - 8 q^{82} + 32 q^{86} + 8 q^{88} - 88 q^{92} + 40 q^{97} + O(q^{100}) \)

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

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