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Properties

Label 2200.2.r
Level $2200$
Weight $2$
Character orbit 2200.r
Rep. character $\chi_{2200}(243,\cdot)$
Character field $\Q(\zeta_{4})$
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.r (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
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 744 360 384
Cusp forms 696 360 336
Eisenstein series 48 0 48

Trace form

\( 360 q - 16 q^{6} + 12 q^{8} + O(q^{10}) \) \( 360 q - 16 q^{6} + 12 q^{8} + 32 q^{16} - 8 q^{17} + 28 q^{18} + 16 q^{26} - 20 q^{28} - 40 q^{32} - 64 q^{36} + 16 q^{38} - 80 q^{42} - 48 q^{46} + 48 q^{48} + 64 q^{51} + 76 q^{52} - 16 q^{56} + 56 q^{58} + 36 q^{62} - 48 q^{67} + 52 q^{68} - 20 q^{72} + 40 q^{73} + 16 q^{76} - 104 q^{78} - 296 q^{81} - 40 q^{82} - 192 q^{86} + 24 q^{88} - 64 q^{91} - 16 q^{92} + 80 q^{96} + 8 q^{97} - 88 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)