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

• Label: 352.2.bf
• Level: $352$
• Weight: $2$
• Character orbit: 352.bf
• Rep. character: $\chi_{352}(5,\cdot)$
• Character field: $\Q(\zeta_{40})$
• Dimension: $736$
• 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.bf (of order \(40\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 352 \)
Character field:			\(\Q(\zeta_{40})\)
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	800	800	0
Cusp forms	736	736	0
Eisenstein series	64	64	0

Trace form

736 * q - 12 * q^2 - 12 * q^3 - 12 * q^4 - 12 * q^5 - 12 * q^6 - 12 * q^7 - 12 * q^8 - 12 * q^9 - 32 * q^10 - 16 * q^11 - 64 * q^12 - 12 * q^13 - 28 * q^14 - 52 * q^16 + 48 * q^18 - 12 * q^19 - 28 * q^20 - 32 * q^21 - 28 * q^22 - 48 * q^23 - 12 * q^24 - 12 * q^25 - 72 * q^26 - 12 * q^27 - 12 * q^28 - 12 * q^29 - 28 * q^30 - 24 * q^31 + 8 * q^32 - 32 * q^33 - 8 * q^34 - 12 * q^35 - 12 * q^36 - 12 * q^37 - 12 * q^38 - 12 * q^39 + 28 * q^40 - 12 * q^41 - 52 * q^42 - 48 * q^43 - 56 * q^44 - 56 * q^45 - 76 * q^46 - 12 * q^48 - 12 * q^50 - 36 * q^51 - 28 * q^52 + 36 * q^53 - 120 * q^54 + 16 * q^55 + 184 * q^56 - 12 * q^57 - 12 * q^58 + 20 * q^59 + 4 * q^60 - 12 * q^61 + 4 * q^62 + 56 * q^63 - 156 * q^64 - 64 * q^65 + 8 * q^66 + 48 * q^67 - 100 * q^68 - 12 * q^69 + 36 * q^70 + 20 * q^71 + 168 * q^72 - 12 * q^73 - 44 * q^74 - 148 * q^75 - 32 * q^76 - 32 * q^77 + 16 * q^78 - 148 * q^80 - 52 * q^82 - 12 * q^83 + 100 * q^84 - 52 * q^85 + 92 * q^86 - 32 * q^87 - 20 * q^88 - 32 * q^89 - 180 * q^90 + 132 * q^91 + 132 * q^92 + 12 * q^93 + 8 * q^94 - 152 * q^95 - 76 * q^96 - 24 * q^97 - 48 * q^98 - 68 * q^99

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.bf.a	$352$	$2$	352.bf	352.af	$40$	$736$	$46$	$2.811$		None		✓	✓	✓	352.2.bf.a	$4$	$0$	\(-12\)	\(-12\)	\(-12\)	\(-12\)		$\mathrm{SU}(2)[C_{40}]$