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

• Label: 1280.2.j
• Level: $1280$
• Weight: $2$
• Character orbit: 1280.j
• Rep. character: $\chi_{1280}(63,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $96$
• Newform subspaces: $4$
• Sturm bound: $384$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1280.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 80 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(384\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(3\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	432	96	336
Cusp forms	336	96	240
Eisenstein series	96	0	96

Trace form

\( 96 q - 96 q^{9} + O(q^{10}) \)

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

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1280.2.j.a	$1280$	$2$	1280.j	80.j	$4$	$16$	$8$	$10.221$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\beta _{9}-\beta _{12})q^{3}+(\beta _{5}-\beta _{6})q^{5}+\beta _{2}q^{7}+\cdots\)
1280.2.j.b	$1280$	$2$	1280.j	80.j	$4$	$16$	$8$	$10.221$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\beta _{9}-\beta _{12})q^{3}+(-\beta _{5}+\beta _{6})q^{5}+\cdots\)
1280.2.j.c	$1280$	$2$	1280.j	80.j	$4$	$32$	$16$	$10.221$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
1280.2.j.d	$1280$	$2$	1280.j	80.j	$4$	$32$	$16$	$10.221$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(1280, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)