Space of modular forms of level 3648, weight 2, and Character 3648.ds

• Label: 3648.2.ds
• Level: $3648$
• Weight: $2$
• Character orbit: 3648.ds
• Rep. character: $\chi_{3648}(259,\cdot)$
• Character field: $\Q(\zeta_{48})$
• Dimension: $5120$
• Sturm bound: $1280$

Defining parameters

Level:	\( N \)	\(=\)	\( 3648 = 2^{6} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3648.ds (of order \(48\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1216 \)
Character field:			\(\Q(\zeta_{48})\)
Sturm bound:			\(1280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3648, [\chi])\).

	Total	New	Old
Modular forms	10304	5120	5184
Cusp forms	10176	5120	5056
Eisenstein series	128	0	128

Trace form

\( 5120 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3648, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3648, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3648, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1216, [\chi])\)\(^{\oplus 2}\)