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Properties

Label 384.8.j
Level $384$
Weight $8$
Character orbit 384.j
Rep. character $\chi_{384}(97,\cdot)$
Character field $\Q(\zeta_{4})$
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.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
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 928 112 816
Cusp forms 864 112 752
Eisenstein series 64 0 64

Trace form

\( 112 q + O(q^{10}) \) \( 112 q - 206752 q^{29} + 1662304 q^{37} - 13176688 q^{49} + 3631264 q^{53} + 4559776 q^{61} + 5707552 q^{65} - 9580896 q^{69} + 23828896 q^{77} - 59521392 q^{81} + 15068000 q^{85} + O(q^{100}) \)

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

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