Space of modular forms of level 1280, weight 2, and Character 1280.z

• Label: 1280.2.z
• Level: $1280$
• Weight: $2$
• Character orbit: 1280.z
• Rep. character: $\chi_{1280}(289,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $176$
• Sturm bound: $384$

Defining parameters

Level:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1280.z (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 160 \)
Character field:			\(\Q(\zeta_{8})\)
Sturm bound:			\(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1280, [\chi])\).

	Total	New	Old
Modular forms	832	208	624
Cusp forms	704	176	528
Eisenstein series	128	32	96

Trace form

\( 176 q + 8 q^{5} - 16 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1280, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1280, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1280, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 2}\)