↑

Properties

Label 2200.2.bb
Level $2200$
Weight $2$
Character orbit 2200.bb
Rep. character $\chi_{2200}(81,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $360$
Sturm bound $720$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2200 = 2^{3} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2200.bb (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{5})\)
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

\( 360 q - 2 q^{7} - 90 q^{9} + O(q^{10}) \) \( 360 q - 2 q^{7} - 90 q^{9} - 12 q^{15} - 12 q^{19} + 8 q^{21} + 6 q^{23} - 4 q^{25} + 18 q^{27} + 12 q^{29} - 2 q^{31} - 60 q^{33} - 12 q^{35} - 24 q^{37} + 16 q^{41} + 22 q^{45} - 16 q^{47} - 84 q^{49} - 24 q^{51} - 12 q^{53} + 56 q^{55} - 52 q^{57} + 12 q^{61} + 32 q^{63} - 6 q^{65} + 28 q^{67} - 12 q^{69} - 4 q^{71} - 24 q^{73} + 22 q^{75} + 16 q^{77} - 48 q^{79} - 90 q^{81} - 84 q^{83} + 2 q^{85} - 24 q^{91} + 84 q^{93} - 36 q^{95} + 20 q^{99} + O(q^{100}) \)

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

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