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Properties

Label 384.8.k
Level $384$
Weight $8$
Character orbit 384.k
Rep. character $\chi_{384}(95,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $216$
Sturm bound $512$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 384.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Sturm bound: \(512\)

Dimensions

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

Total New Old
Modular forms 928 232 696
Cusp forms 864 216 648
Eisenstein series 64 16 48

Trace form

\( 216 q + O(q^{10}) \) \( 216 q + 8 q^{13} + 8752 q^{21} - 8 q^{33} + 8 q^{37} + 312504 q^{45} + 19765016 q^{49} + 4559784 q^{61} - 8744 q^{69} - 8 q^{81} - 15692992 q^{85} + 28990792 q^{93} - 16 q^{97} + O(q^{100}) \)

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

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