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Properties

Label 2200.2.eh
Level $2200$
Weight $2$
Character orbit 2200.eh
Rep. character $\chi_{2200}(221,\cdot)$
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.eh (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

\( 1200 q + 18 q^{8} + 300 q^{9} + O(q^{10}) \) \( 1200 q + 18 q^{8} + 300 q^{9} - 6 q^{10} + 12 q^{14} + 8 q^{17} + 28 q^{18} - 8 q^{20} + 28 q^{24} - 4 q^{25} + 44 q^{28} - 98 q^{30} - 24 q^{31} + 40 q^{32} - 32 q^{34} + 60 q^{36} + 24 q^{38} - 36 q^{40} - 8 q^{41} - 100 q^{42} + 40 q^{46} + 48 q^{47} + 74 q^{48} + 1200 q^{49} - 84 q^{50} - 6 q^{52} - 78 q^{54} + 36 q^{56} - 68 q^{58} + 170 q^{60} - 36 q^{62} + 42 q^{64} + 84 q^{65} + 52 q^{68} - 24 q^{70} + 56 q^{71} - 50 q^{72} + 40 q^{73} + 28 q^{74} - 60 q^{76} - 178 q^{78} - 150 q^{80} - 300 q^{81} - 124 q^{84} - 70 q^{86} - 112 q^{87} - 36 q^{88} - 60 q^{89} - 94 q^{90} + 24 q^{92} - 20 q^{94} - 24 q^{95} + 80 q^{96} + 8 q^{97} + 64 q^{98} + O(q^{100}) \)

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

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