Space of modular forms of level 200, weight 3, and Character 200.x

• Label: 200.3.x
• Level: $200$
• Weight: $3$
• Character orbit: 200.x
• Rep. character: $\chi_{200}(13,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $464$
• Newform subspaces: $1$
• Sturm bound: $90$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	200.x (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 200 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(90\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(200, [\chi])\).

	Total	New	Old
Modular forms	496	496	0
Cusp forms	464	464	0
Eisenstein series	32	32	0

Trace form

464 * q - 8 * q^2 - 10 * q^4 - 6 * q^6 - 16 * q^7 - 14 * q^8 - 20 * q^9 - 16 * q^10 + 34 * q^12 - 10 * q^14 - 16 * q^15 - 6 * q^16 - 8 * q^17 - 20 * q^18 + 14 * q^20 - 102 * q^22 - 16 * q^23 + 8 * q^25 - 16 * q^26 - 78 * q^28 - 110 * q^30 - 12 * q^31 - 138 * q^32 - 52 * q^33 - 10 * q^34 - 70 * q^36 - 152 * q^38 - 20 * q^39 + 284 * q^40 - 12 * q^41 - 426 * q^42 + 340 * q^44 - 6 * q^46 - 208 * q^47 + 376 * q^48 + 354 * q^50 + 52 * q^52 + 640 * q^54 - 116 * q^55 - 6 * q^56 + 20 * q^57 + 352 * q^58 - 770 * q^60 + 304 * q^62 - 248 * q^63 - 460 * q^64 + 40 * q^65 - 150 * q^66 - 406 * q^68 - 310 * q^70 - 12 * q^71 - 768 * q^72 + 104 * q^73 + 48 * q^76 + 448 * q^78 - 20 * q^79 - 506 * q^80 + 744 * q^81 - 14 * q^82 - 1210 * q^84 - 6 * q^86 + 468 * q^87 - 1026 * q^88 - 1020 * q^89 - 886 * q^90 - 82 * q^92 - 810 * q^94 + 468 * q^95 + 54 * q^96 + 40 * q^97 - 656 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(200, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
200.3.x.a	$200$	$3$	200.x	200.x	$20$	$464$	$58$	$5.450$		None		✓	✓	✓	200.3.x.a	$4$	$0$	\(-8\)	\(0\)	\(0\)	\(-16\)		$\mathrm{SU}(2)[C_{20}]$