Space of modular forms of level 1536, weight 2, and Character 1536.bd

• Label: 1536.2.bd
• Level: $1536$
• Weight: $2$
• Character orbit: 1536.bd
• Rep. character: $\chi_{1536}(13,\cdot)$
• Character field: $\Q(\zeta_{128})$
• Dimension: $8192$
• Sturm bound: $512$

Defining parameters

Level:	\( N \)	\(=\)	\( 1536 = 2^{9} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1536.bd (of order \(128\) and degree \(64\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 512 \)
Character field:			\(\Q(\zeta_{128})\)
Sturm bound:			\(512\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1536, [\chi])\).

	Total	New	Old
Modular forms	16512	8192	8320
Cusp forms	16256	8192	8064
Eisenstein series	256	0	256

Trace form

\( 8192 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1536, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1536, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1536, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(512, [\chi])\)\(^{\oplus 2}\)