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Properties

Label 2200.2.bn
Level $2200$
Weight $2$
Character orbit 2200.bn
Rep. character $\chi_{2200}(309,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $1200$
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.bn (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 200 \)
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 1456 1200 256
Cusp forms 1424 1200 224
Eisenstein series 32 0 32

Trace form

\( 1200 q - 30 q^{8} - 300 q^{9} + O(q^{10}) \) \( 1200 q - 30 q^{8} - 300 q^{9} + 6 q^{10} + 12 q^{14} + 8 q^{20} + 28 q^{24} - 4 q^{25} + 58 q^{30} + 24 q^{31} - 32 q^{34} - 60 q^{36} - 100 q^{38} - 4 q^{40} + 8 q^{41} - 100 q^{42} - 40 q^{46} + 130 q^{48} - 1200 q^{49} - 20 q^{50} + 190 q^{52} - 78 q^{54} - 36 q^{56} + 60 q^{58} + 30 q^{60} + 42 q^{64} - 76 q^{65} - 32 q^{70} - 56 q^{71} + 150 q^{72} + 28 q^{74} + 60 q^{76} + 130 q^{78} + 166 q^{80} - 300 q^{81} - 124 q^{84} + 70 q^{86} - 60 q^{88} - 60 q^{89} - 146 q^{90} - 140 q^{92} + 20 q^{94} - 24 q^{95} - 40 q^{96} + O(q^{100}) \)

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

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