Space of modular forms of level 128, weight 2, and Character 128.k

• Label: 128.2.k
• Level: $128$
• Weight: $2$
• Character orbit: 128.k
• Rep. character: $\chi_{128}(5,\cdot)$
• Character field: $\Q(\zeta_{32})$
• Dimension: $240$
• Newform subspaces: $1$
• Sturm bound: $32$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	128.k (of order \(32\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 128 \)
Character field:			\(\Q(\zeta_{32})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(32\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(128, [\chi])\).

	Total	New	Old
Modular forms	272	272	0
Cusp forms	240	240	0
Eisenstein series	32	32	0

Trace form

\( 240 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(128, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
128.2.k.a	$128$	$2$	128.k	128.k	$32$	$240$	$15$	$1.022$		None		$2$	$0$	\(-16\)	\(-16\)	\(-16\)	\(-16\)		$\mathrm{SU}(2)[C_{32}]$