Space of modular forms of level 1280, weight 3, and Character 1280.i

• Label: 1280.3.i
• Level: $1280$
• Weight: $3$
• Character orbit: 1280.i
• Rep. character: $\chi_{1280}(833,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $192$
• Sturm bound: $576$

Defining parameters

Level:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1280.i (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 80 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1280, [\chi])\).

	Total	New	Old
Modular forms	816	192	624
Cusp forms	720	192	528
Eisenstein series	96	0	96

Trace form

\( 192 q - 576 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1280, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1280, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1280, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)