Properties

Label 900.3.q
Level $900$
Weight $3$
Character orbit 900.q
Rep. character $\chi_{900}(499,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $424$
Sturm bound $540$

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Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 900.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 180 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(540\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(900, [\chi])\).

Total New Old
Modular forms 744 440 304
Cusp forms 696 424 272
Eisenstein series 48 16 32

Trace form

\( 424q + 2q^{4} - 12q^{6} + 8q^{9} + O(q^{10}) \) \( 424q + 2q^{4} - 12q^{6} + 8q^{9} + 18q^{14} - 2q^{16} - 28q^{21} - 86q^{24} - 88q^{26} - 44q^{29} - 2q^{34} + 240q^{36} - 4q^{41} - 504q^{44} + 144q^{46} - 1312q^{49} + 374q^{54} + 12q^{56} - 4q^{61} + 272q^{64} - 398q^{66} + 396q^{69} - 284q^{74} - 126q^{76} - 408q^{81} + 142q^{84} - 210q^{86} - 464q^{89} + 138q^{94} - 972q^{96} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)