Space of modular forms of level 384, weight 8, and Character 384.v

• Label: 384.8.v
• Level: $384$
• Weight: $8$
• Character orbit: 384.v
• Rep. character: $\chi_{384}(13,\cdot)$
• Character field: $\Q(\zeta_{32})$
• Dimension: $3584$
• Sturm bound: $512$

Defining parameters

Level:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 128 \)
Character field:			\(\Q(\zeta_{32})\)
Sturm bound:			\(512\)

Dimensions

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

	Total	New	Old
Modular forms	7200	3584	3616
Cusp forms	7136	3584	3552
Eisenstein series	64	0	64

Trace form

\( 3584 q + O(q^{10}) \)

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

\( S_{8}^{\mathrm{old}}(384, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)