Space of modular forms of level 3072, weight 2, and Character 3072.bh

• Label: 3072.2.bh
• Level: $3072$
• Weight: $2$
• Character orbit: 3072.bh
• Rep. character: $\chi_{3072}(13,\cdot)$
• Character field: $\Q(\zeta_{256})$
• Dimension: $32768$
• Sturm bound: $1024$

Defining parameters

Level:	\( N \)	\(=\)	\( 3072 = 2^{10} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3072.bh (of order \(256\) and degree \(128\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1024 \)
Character field:			\(\Q(\zeta_{256})\)
Sturm bound:			\(1024\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3072, [\chi])\).

	Total	New	Old
Modular forms	65792	32768	33024
Cusp forms	65280	32768	32512
Eisenstein series	512	0	512

Trace form

\( 32768 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3072, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3072, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3072, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1024, [\chi])\)\(^{\oplus 2}\)