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

• Label: 3840.2.bs
• Level: $3840$
• Weight: $2$
• Character orbit: 3840.bs
• Rep. character: $\chi_{3840}(479,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $736$
• Sturm bound: $1536$

Defining parameters

Level:	\( N \)	\(=\)	\( 3840 = 2^{8} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3840.bs (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 480 \)
Character field:			\(\Q(\zeta_{8})\)
Sturm bound:			\(1536\)

Dimensions

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

	Total	New	Old
Modular forms	3200	800	2400
Cusp forms	2944	736	2208
Eisenstein series	256	64	192

Trace form

\( 736 q - 16 q^{9} + O(q^{10}) \)

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

\( S_{2}^{\mathrm{old}}(3840, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1920, [\chi])\)\(^{\oplus 2}\)