Space of modular forms of level 352, weight 2, and Character 352.n

• Label: 352.2.n
• Level: $352$
• Weight: $2$
• Character orbit: 352.n
• Rep. character: $\chi_{352}(45,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $160$
• Newform subspaces: $1$
• Sturm bound: $96$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	352.n (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 32 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(96\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(352, [\chi])\).

	Total	New	Old
Modular forms	200	160	40
Cusp forms	184	160	24
Eisenstein series	16	0	16

Trace form

160 * q - 16 * q^10 - 16 * q^14 - 16 * q^20 + 24 * q^24 - 48 * q^27 + 40 * q^28 + 80 * q^30 - 48 * q^31 - 48 * q^35 + 56 * q^36 - 16 * q^38 - 48 * q^39 - 64 * q^40 - 104 * q^48 - 80 * q^50 + 32 * q^51 + 64 * q^54 - 40 * q^56 + 8 * q^58 + 32 * q^59 - 8 * q^60 - 64 * q^61 + 24 * q^62 - 24 * q^64 + 48 * q^68 - 64 * q^69 - 24 * q^70 + 32 * q^71 + 72 * q^72 - 128 * q^78 - 16 * q^80 + 40 * q^82 - 80 * q^83 - 152 * q^84 - 64 * q^86 - 112 * q^87 + 144 * q^90 - 72 * q^92 + 96 * q^94 + 56 * q^96 + 56 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(352, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
352.2.n.a	$352$	$2$	352.n	32.g	$8$	$160$	$40$	$2.811$		None		✓	✓	✓	352.2.n.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{2}^{\mathrm{old}}(352, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(352, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)