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Properties

Label 1800.2.bg
Level $1800$
Weight $2$
Character orbit 1800.bg
Rep. character $\chi_{1800}(301,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $444$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1800.bg (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 72 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1800, [\chi])\).

Total New Old
Modular forms 744 468 276
Cusp forms 696 444 252
Eisenstein series 48 24 24

Trace form

\( 444 q + q^{2} + q^{4} - q^{6} + 2 q^{7} - 2 q^{8} + 4 q^{9} + O(q^{10}) \) \( 444 q + q^{2} + q^{4} - q^{6} + 2 q^{7} - 2 q^{8} + 4 q^{9} - 6 q^{12} + 18 q^{14} - 3 q^{16} + 8 q^{17} - 12 q^{18} + 5 q^{22} - 10 q^{23} + 9 q^{24} - 12 q^{26} - 4 q^{28} - 6 q^{31} + q^{32} + 2 q^{33} + q^{34} + 27 q^{36} - 5 q^{38} - 2 q^{39} - 2 q^{41} - 30 q^{42} + 2 q^{44} - 4 q^{46} + 22 q^{47} + 37 q^{48} - 184 q^{49} + 18 q^{52} + 51 q^{54} + 10 q^{56} - 12 q^{57} - 4 q^{58} - 8 q^{62} + 30 q^{63} + 10 q^{64} + 34 q^{66} + 23 q^{68} - 80 q^{71} - 39 q^{72} + 8 q^{73} + 14 q^{74} + 3 q^{76} - 92 q^{78} + 2 q^{79} + 18 q^{82} + 46 q^{84} + 19 q^{86} + 6 q^{87} - 19 q^{88} - 8 q^{89} - 6 q^{92} + 34 q^{94} + 98 q^{96} + 2 q^{97} - 78 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1800, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1800, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)