Space of modular forms of level 800, weight 2, and Character 800.by

• Label: 800.2.by
• Level: $800$
• Weight: $2$
• Character orbit: 800.by
• Rep. character: $\chi_{800}(29,\cdot)$
• Character field: $\Q(\zeta_{40})$
• Dimension: $1888$
• Newform subspaces: $1$
• Sturm bound: $240$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.by (of order \(40\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 800 \)
Character field:			\(\Q(\zeta_{40})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(240\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(800, [\chi])\).

	Total	New	Old
Modular forms	1952	1952	0
Cusp forms	1888	1888	0
Eisenstein series	64	64	0

Trace form

1888 * q - 20 * q^2 - 20 * q^3 - 12 * q^4 - 16 * q^5 - 12 * q^6 - 20 * q^8 - 12 * q^9 - 16 * q^10 - 12 * q^11 - 20 * q^12 - 20 * q^13 - 12 * q^14 - 12 * q^16 - 12 * q^19 - 16 * q^20 - 12 * q^21 - 20 * q^22 - 20 * q^23 - 32 * q^24 - 16 * q^25 - 72 * q^26 - 20 * q^27 - 20 * q^28 - 12 * q^29 + 32 * q^30 + 24 * q^31 - 40 * q^33 + 4 * q^34 - 40 * q^35 + 108 * q^36 - 20 * q^37 - 160 * q^38 - 12 * q^39 - 64 * q^40 - 12 * q^41 - 20 * q^42 - 12 * q^44 - 4 * q^45 - 12 * q^46 + 240 * q^48 + 24 * q^50 - 8 * q^51 - 20 * q^52 - 20 * q^53 - 12 * q^54 - 48 * q^55 - 12 * q^56 - 20 * q^58 - 12 * q^59 - 192 * q^60 - 12 * q^61 - 20 * q^62 - 40 * q^63 + 24 * q^64 - 32 * q^65 - 28 * q^66 - 20 * q^67 - 12 * q^69 - 100 * q^70 - 12 * q^71 - 20 * q^72 - 20 * q^73 - 120 * q^74 - 48 * q^75 - 32 * q^76 - 20 * q^77 - 20 * q^78 - 68 * q^80 - 20 * q^83 - 164 * q^84 + 4 * q^85 - 12 * q^86 - 20 * q^87 - 240 * q^88 - 12 * q^89 - 100 * q^90 - 12 * q^91 - 200 * q^92 - 92 * q^94 - 32 * q^95 - 132 * q^96 - 40 * q^97 + 20 * q^98 - 56 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(800, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
800.2.by.a	$800$	$2$	800.by	800.ay	$40$	$1888$	$118$	$6.388$		None		✓	✓	✓	800.2.by.a	$4$	$0$	\(-20\)	\(-20\)	\(-16\)	\(0\)		$\mathrm{SU}(2)[C_{40}]$