Space of modular forms of level 1280, weight 4, and Character 1280.c

• Label: 1280.4.c
• Level: $1280$
• Weight: $4$
• Character orbit: 1280.c
• Rep. character: $\chi_{1280}(769,\cdot)$
• Character field: $\Q$
• Dimension: $140$
• Sturm bound: $768$

Defining parameters

Level:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1280.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Sturm bound:			\(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1280, [\chi])\).

	Total	New	Old
Modular forms	600	148	452
Cusp forms	552	140	412
Eisenstein series	48	8	40

Trace form

\( 140 q - 1180 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1280, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1280, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1280, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 2}\)