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Properties

Label 2200.2.dj
Level $2200$
Weight $2$
Character orbit 2200.dj
Rep. character $\chi_{2200}(301,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $888$
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.dj (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 88 \)
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 936 552
Cusp forms 1392 888 504
Eisenstein series 96 48 48

Trace form

\( 888 q + q^{2} + 5 q^{4} - 5 q^{6} + 2 q^{7} + q^{8} + 216 q^{9} + O(q^{10}) \) \( 888 q + q^{2} + 5 q^{4} - 5 q^{6} + 2 q^{7} + q^{8} + 216 q^{9} + 6 q^{12} + 8 q^{14} - 7 q^{16} + 6 q^{17} - 10 q^{18} - 21 q^{22} + 24 q^{23} - 13 q^{24} - 2 q^{26} + 22 q^{28} - 18 q^{31} + 16 q^{32} + 18 q^{33} + 2 q^{34} - 38 q^{36} - 2 q^{38} - 14 q^{39} - 26 q^{41} + 22 q^{42} + 68 q^{44} + 42 q^{46} + 6 q^{47} + 36 q^{48} - 180 q^{49} + 66 q^{52} - 104 q^{54} - 40 q^{56} + 10 q^{57} + 70 q^{58} - 24 q^{62} - 20 q^{63} + 65 q^{64} - 2 q^{66} - 36 q^{68} - 22 q^{71} - 25 q^{72} + 6 q^{73} - 64 q^{74} - 98 q^{76} + 128 q^{78} + 46 q^{79} - 172 q^{81} - 77 q^{82} - 108 q^{84} - 33 q^{86} + 124 q^{87} + 57 q^{88} + 16 q^{89} - 60 q^{92} + 68 q^{94} - 94 q^{96} - 10 q^{97} + 68 q^{98} + O(q^{100}) \)

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

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