Properties

Label 384.9.u
Level $384$
Weight $9$
Character orbit 384.u
Rep. character $\chi_{384}(19,\cdot)$
Character field $\Q(\zeta_{32})$
Dimension $4096$
Sturm bound $576$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 384.u (of order \(32\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 128 \)
Character field: \(\Q(\zeta_{32})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(384, [\chi])\).

Total New Old
Modular forms 8224 4096 4128
Cusp forms 8160 4096 4064
Eisenstein series 64 0 64

Trace form

\( 4096 q + O(q^{10}) \) \( 4096 q - 20580768 q^{50} - 91896288 q^{52} + 39680928 q^{54} + 227499552 q^{56} - 327416256 q^{60} - 175726656 q^{62} + 193535808 q^{64} + 454631616 q^{66} + 327458880 q^{68} - 185779776 q^{70} - 680115744 q^{74} + 79651936 q^{76} + 735959520 q^{78} - 808638048 q^{80} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(384, [\chi])\) into newform subspaces

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

Decomposition of \(S_{9}^{\mathrm{old}}(384, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)