Properties

Label 900.3.bd
Level $900$
Weight $3$
Character orbit 900.bd
Rep. character $\chi_{900}(407,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $848$
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.bd (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 180 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(540\)

Dimensions

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

Total New Old
Modular forms 1488 880 608
Cusp forms 1392 848 544
Eisenstein series 96 32 64

Trace form

\( 848q + 6q^{2} - 8q^{6} + O(q^{10}) \) \( 848q + 6q^{2} - 8q^{6} - 14q^{12} + 4q^{13} - 4q^{16} + 24q^{18} - 48q^{21} - 14q^{22} - 56q^{28} + 186q^{32} - 28q^{33} + 152q^{36} + 16q^{37} + 30q^{38} - 24q^{41} - 178q^{42} - 352q^{46} + 202q^{48} + 66q^{52} + 492q^{56} + 48q^{57} - 14q^{58} - 8q^{61} + 576q^{66} + 102q^{68} - 210q^{72} + 16q^{73} - 380q^{76} + 12q^{77} + 510q^{78} + 144q^{81} + 24q^{82} + 636q^{86} + 106q^{88} - 336q^{92} - 628q^{93} + 256q^{96} + 4q^{97} + O(q^{100}) \)

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

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