Properties

Label 432.8.k
Level $432$
Weight $8$
Character orbit 432.k
Rep. character $\chi_{432}(109,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $448$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 432.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(432, [\chi])\).

Total New Old
Modular forms 1020 448 572
Cusp forms 996 448 548
Eisenstein series 24 0 24

Trace form

\( 448 q + 6500 q^{10} - 97500 q^{16} + 60584 q^{19} + 24268 q^{22} + 285276 q^{28} + 1025708 q^{34} - 1793564 q^{40} + 752848 q^{43} - 1528080 q^{46} - 52706752 q^{49} + 678940 q^{52} + 11311536 q^{58} + 2279888 q^{61}+ \cdots + 44341116 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{8}^{\mathrm{new}}(432, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(432, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(432, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)