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Properties

Label 384.9.m
Level $384$
Weight $9$
Character orbit 384.m
Rep. character $\chi_{384}(79,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $256$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 384.m (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 2080 256 1824
Cusp forms 2016 256 1760
Eisenstein series 64 0 64

Trace form

\( 256 q + O(q^{10}) \) \( 256 q + 1691136 q^{23} - 4831488 q^{35} - 3719424 q^{43} - 27724032 q^{51} + 10717440 q^{53} + 46326784 q^{55} - 89877504 q^{59} - 48952064 q^{61} + 37352192 q^{67} + 17273088 q^{69} - 159664128 q^{71} - 25837056 q^{75} + 189928704 q^{77} + 144406528 q^{79} + 350400768 q^{91} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{9}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)