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

• Label: 3840.2.cn
• Level: $3840$
• Weight: $2$
• Character orbit: 3840.cn
• Rep. character: $\chi_{3840}(431,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $1024$
• Sturm bound: $1536$

Defining parameters

Level:	\( N \)	\(=\)	\( 3840 = 2^{8} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3840.cn (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 192 \)
Character field:			\(\Q(\zeta_{16})\)
Sturm bound:			\(1536\)

Dimensions

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

	Total	New	Old
Modular forms	6272	1024	5248
Cusp forms	6016	1024	4992
Eisenstein series	256	0	256

Trace form

\( 1024 q + O(q^{10}) \)

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

\( S_{2}^{\mathrm{old}}(3840, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1920, [\chi])\)\(^{\oplus 2}\)