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Properties

Label 2200.2.ea
Level $2200$
Weight $2$
Character orbit 2200.ea
Rep. character $\chi_{2200}(299,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $848$
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.ea (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 440 \)
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 1488 880 608
Cusp forms 1392 848 544
Eisenstein series 96 32 64

Trace form

\( 848 q + 6 q^{4} - 10 q^{6} + 216 q^{9} + O(q^{10}) \) \( 848 q + 6 q^{4} - 10 q^{6} + 216 q^{9} - 16 q^{11} + 6 q^{14} - 22 q^{16} + 20 q^{19} + 10 q^{24} + 72 q^{26} + 56 q^{34} - 56 q^{36} - 20 q^{41} - 54 q^{44} + 40 q^{46} + 200 q^{49} - 20 q^{51} - 88 q^{56} + 44 q^{59} + 42 q^{64} - 124 q^{66} - 130 q^{74} - 168 q^{81} - 20 q^{84} - 18 q^{86} + 32 q^{89} + 76 q^{91} - 60 q^{94} + 160 q^{96} + 32 q^{99} + O(q^{100}) \)

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

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