Properties

Label 2200.2.eb
Level $2200$
Weight $2$
Character orbit 2200.eb
Rep. character $\chi_{2200}(889,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $360$
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.eb (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
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 1472 360 1112
Cusp forms 1408 360 1048
Eisenstein series 64 0 64

Trace form

\( 360 q + 10 q^{7} + 90 q^{9} + O(q^{10}) \) \( 360 q + 10 q^{7} + 90 q^{9} + 28 q^{15} - 12 q^{19} - 8 q^{21} + 30 q^{23} - 10 q^{25} + 12 q^{29} + 12 q^{31} + 30 q^{33} + 12 q^{35} + 64 q^{41} + 10 q^{45} + 96 q^{49} + 24 q^{51} - 30 q^{53} - 8 q^{55} - 20 q^{57} - 12 q^{61} - 30 q^{65} - 60 q^{67} + 18 q^{69} - 16 q^{71} + 62 q^{75} + 30 q^{77} + 32 q^{79} - 90 q^{81} - 30 q^{83} - 60 q^{87} - 16 q^{91} - 8 q^{95} - 30 q^{97} + 20 q^{99} + O(q^{100}) \)

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

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