Properties

Label 900.6.o
Level $900$
Weight $6$
Character orbit 900.o
Rep. character $\chi_{900}(299,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $1072$
Sturm bound $1080$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 900.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 180 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(900, [\chi])\).

Total New Old
Modular forms 1824 1088 736
Cusp forms 1776 1072 704
Eisenstein series 48 16 32

Trace form

\( 1072 q + 2 q^{4} + 60 q^{6} + 8 q^{9} + O(q^{10}) \) \( 1072 q + 2 q^{4} + 60 q^{6} + 8 q^{9} + 6 q^{14} - 2 q^{16} - 2620 q^{21} + 670 q^{24} - 23868 q^{29} + 12598 q^{34} - 7896 q^{36} - 12 q^{41} + 54000 q^{46} - 1229308 q^{49} + 200174 q^{54} - 244068 q^{56} - 4 q^{61} - 107872 q^{64} + 113038 q^{66} - 164340 q^{69} - 258144 q^{74} - 48294 q^{76} + 471840 q^{81} - 75638 q^{84} - 555006 q^{86} + 57738 q^{94} + 536904 q^{96} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)