Space of modular forms of level 3584, weight 2, and Character 3584.bi

• Label: 3584.2.bi
• Level: $3584$
• Weight: $2$
• Character orbit: 3584.bi
• Rep. character: $\chi_{3584}(703,\cdot)$
• Character field: $\Q(\zeta_{24})$
• Dimension: $960$
• Sturm bound: $1024$

Defining parameters

Level:	\( N \)	\(=\)	\( 3584 = 2^{9} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3584.bi (of order \(24\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 224 \)
Character field:			\(\Q(\zeta_{24})\)
Sturm bound:			\(1024\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3584, [\chi])\).

	Total	New	Old
Modular forms	4352	1088	3264
Cusp forms	3840	960	2880
Eisenstein series	512	128	384

Trace form

\( 960 q + 16 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3584, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3584, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3584, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(896, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1792, [\chi])\)\(^{\oplus 2}\)