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Properties

Label 432.9.bi
Level $432$
Weight $9$
Character orbit 432.bi
Rep. character $\chi_{432}(5,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $6888$
Sturm bound $648$

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Defining parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 432.bi (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 432 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(648\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(432, [\chi])\).

Total New Old
Modular forms 6936 6936 0
Cusp forms 6888 6888 0
Eisenstein series 48 48 0

Trace form

\( 6888 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 18 q^{8} - 6 q^{10} - 12 q^{11} - 25842 q^{12} - 12 q^{13} - 12 q^{14} - 24 q^{15} - 12 q^{16} - 36 q^{17} - 12 q^{18} - 6 q^{19} + 628854 q^{20}+ \cdots - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{9}^{\mathrm{new}}(432, [\chi])\) into newform subspaces

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