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 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 + 32 * q^50 - 16 * q^51 + 80 * q^52 - 16 * q^53 + 112 * q^54 - 16 * q^55 + 96 * q^56 - 16 * q^57 + 128 * q^58 - 16 * q^59 + 176 * q^60 - 16 * q^61 + 80 * q^62 + 176 * q^64 + 176 * q^66 - 16 * q^67 + 80 * q^68 - 16 * q^69 + 176 * q^70 - 16 * q^71 + 128 * q^72 - 16 * q^73 + 96 * q^74 - 16 * q^75 + 112 * q^76 - 16 * q^77 + 80 * q^78 - 16 * q^79 + 32 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	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		✓	✓	✓	128.2.k.a	$2$	$0$	\(-16\)	\(-16\)	\(-16\)	\(-16\)		$\mathrm{SU}(2)[C_{32}]$