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Properties

Label 384.9.l
Level $384$
Weight $9$
Character orbit 384.l
Rep. character $\chi_{384}(31,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $128$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 384.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 1056 128 928
Cusp forms 992 128 864
Eisenstein series 64 0 64

Trace form

\( 128 q + O(q^{10}) \) \( 128 q + 4264704 q^{29} + 9441024 q^{37} + 105413504 q^{49} + 10717440 q^{53} - 48952064 q^{61} + 59883264 q^{65} + 17273088 q^{69} + 189928704 q^{77} - 612220032 q^{81} - 213920000 q^{85} + O(q^{100}) \)

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

\( S_{9}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)