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Properties

Label 384.8.f
Level $384$
Weight $8$
Character orbit 384.f
Rep. character $\chi_{384}(191,\cdot)$
Character field $\Q$
Dimension $112$
Sturm bound $512$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 384.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Sturm bound: \(512\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(384, [\chi])\).

Total New Old
Modular forms 464 112 352
Cusp forms 432 112 320
Eisenstein series 32 0 32

Trace form

\( 112 q + O(q^{10}) \) \( 112 q + 1750000 q^{25} - 198032 q^{33} - 11132496 q^{49} - 1372688 q^{57} - 5068256 q^{73} + 25686960 q^{81} - 8171520 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(384, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(384, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(384, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)