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Properties

Label 2200.2.fo
Level $2200$
Weight $2$
Character orbit 2200.fo
Rep. character $\chi_{2200}(217,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $720$
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.fo (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 2944 720 2224
Cusp forms 2816 720 2096
Eisenstein series 128 0 128

Trace form

\( 720 q + O(q^{10}) \) \( 720 q + 40 q^{15} - 36 q^{23} - 16 q^{25} - 12 q^{27} + 60 q^{33} + 16 q^{37} + 32 q^{45} - 28 q^{47} - 60 q^{49} + 12 q^{53} + 12 q^{55} + 120 q^{57} + 80 q^{63} + 60 q^{65} + 32 q^{67} + 60 q^{69} - 32 q^{75} + 20 q^{77} + 180 q^{81} - 40 q^{85} - 20 q^{87} - 36 q^{93} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1100, [\chi])\)\(^{\oplus 2}\)