↑

Properties

Label 2200.2.p
Level $2200$
Weight $2$
Character orbit 2200.p
Rep. character $\chi_{2200}(1451,\cdot)$
Character field $\Q$
Dimension $222$
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.p (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 88 \)
Character field: \(\Q\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 372 234 138
Cusp forms 348 222 126
Eisenstein series 24 12 12

Trace form

\( 222 q + 4 q^{3} + 214 q^{9} + O(q^{10}) \) \( 222 q + 4 q^{3} + 214 q^{9} - 2 q^{11} - 4 q^{14} - 12 q^{16} - 8 q^{22} - 32 q^{26} + 16 q^{27} + 12 q^{33} + 12 q^{34} - 60 q^{36} - 16 q^{38} + 24 q^{42} + 34 q^{44} + 56 q^{48} + 190 q^{49} + 68 q^{56} - 24 q^{58} + 20 q^{59} - 48 q^{64} + 10 q^{66} + 44 q^{67} + 32 q^{78} + 166 q^{81} - 48 q^{82} + 12 q^{86} + 16 q^{88} + 4 q^{89} + 48 q^{91} + 48 q^{92} - 12 q^{97} + 54 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 2}\)