Space of modular forms of level 3840, weight 2, and Character 3840.ds

• Label: 3840.2.ds
• Level: $3840$
• Weight: $2$
• Character orbit: 3840.ds
• Rep. character: $\chi_{3840}(163,\cdot)$
• Character field: $\Q(\zeta_{64})$
• Dimension: $12288$
• Sturm bound: $1536$

Defining parameters

Level:	\( N \)	\(=\)	\( 3840 = 2^{8} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3840.ds (of order \(64\) and degree \(32\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1280 \)
Character field:			\(\Q(\zeta_{64})\)
Sturm bound:			\(1536\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3840, [\chi])\).

	Total	New	Old
Modular forms	24704	12288	12416
Cusp forms	24448	12288	12160
Eisenstein series	256	0	256

Trace form

\( 12288 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3840, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3840, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3840, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1280, [\chi])\)\(^{\oplus 2}\)