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Properties

Label 1800.2.bn
Level $1800$
Weight $2$
Character orbit 1800.bn
Rep. character $\chi_{1800}(851,\cdot)$
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.bn (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

\( 444 q + 3 q^{2} + 4 q^{3} + q^{4} - 7 q^{6} + 4 q^{9} + O(q^{10}) \) \( 444 q + 3 q^{2} + 4 q^{3} + q^{4} - 7 q^{6} + 4 q^{9} - 18 q^{11} - 12 q^{14} - 3 q^{16} + 20 q^{18} + 8 q^{19} + 5 q^{22} + 15 q^{24} - 8 q^{27} + 12 q^{28} - 27 q^{32} + 18 q^{33} + 13 q^{34} + 31 q^{36} + 39 q^{38} - 30 q^{41} + 20 q^{42} + 2 q^{43} - 28 q^{46} - 33 q^{48} + 188 q^{49} - 4 q^{51} - 11 q^{54} + 54 q^{56} + 12 q^{57} + 6 q^{58} + 42 q^{59} + 34 q^{64} + 6 q^{66} + 2 q^{67} - 63 q^{68} - 15 q^{72} + 8 q^{73} - 9 q^{76} + 18 q^{78} - 16 q^{81} + 26 q^{82} + 66 q^{83} - 70 q^{84} + 75 q^{86} + 5 q^{88} + 4 q^{91} - 24 q^{92} + 10 q^{94} + 10 q^{96} + 2 q^{97} - 10 q^{99} + O(q^{100}) \)

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

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