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Properties

Label 384.8.n
Level $384$
Weight $8$
Character orbit 384.n
Rep. character $\chi_{384}(49,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $224$
Sturm bound $512$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 384.n (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(512\)

Dimensions

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

Total New Old
Modular forms 1824 224 1600
Cusp forms 1760 224 1536
Eisenstein series 64 0 64

Trace form

\( 224 q + O(q^{10}) \) \( 224 q - 286832 q^{23} - 1429968 q^{31} + 1633008 q^{35} + 732368 q^{43} + 2993328 q^{51} + 3631264 q^{53} - 4191008 q^{55} - 3671872 q^{59} + 4559776 q^{61} + 4000752 q^{63} - 776272 q^{67} - 9580896 q^{69} - 24697408 q^{71} + 11260512 q^{75} + 23828896 q^{77} - 3406992 q^{91} + O(q^{100}) \)

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

\( S_{8}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)