Space of modular forms of level 200, weight 6, and Character 200.d

• Label: 200.6.d
• Level: $200$
• Weight: $6$
• Character orbit: 200.d
• Rep. character: $\chi_{200}(101,\cdot)$
• Character field: $\Q$
• Dimension: $92$
• Newform subspaces: $5$
• Sturm bound: $180$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	200.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(180\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(200, [\chi])\).

	Total	New	Old
Modular forms	156	98	58
Cusp forms	144	92	52
Eisenstein series	12	6	6

Trace form

92 * q + 2 * q^4 - 2 * q^6 + 100 * q^7 - 6964 * q^9 + 300 * q^12 + 168 * q^14 + 1218 * q^16 - 200 * q^17 + 540 * q^18 - 8200 * q^22 + 2340 * q^23 + 14382 * q^24 + 5892 * q^26 - 7260 * q^28 + 12920 * q^31 - 12200 * q^32 - 3320 * q^33 - 15838 * q^34 + 3720 * q^36 + 3600 * q^38 + 11744 * q^39 - 7048 * q^41 + 43260 * q^42 + 9286 * q^44 - 16168 * q^46 + 10540 * q^47 + 53240 * q^48 + 192308 * q^49 + 76240 * q^52 + 104166 * q^54 + 24272 * q^56 - 3000 * q^57 - 63280 * q^58 - 94320 * q^62 - 87180 * q^63 + 224114 * q^64 + 113294 * q^66 - 21920 * q^68 - 78304 * q^71 - 152640 * q^72 + 65160 * q^73 + 66388 * q^74 + 44030 * q^76 + 78200 * q^78 + 54632 * q^79 + 411420 * q^81 + 61900 * q^82 - 129880 * q^84 - 196696 * q^86 + 24720 * q^87 + 80320 * q^88 + 84632 * q^89 - 58860 * q^92 - 381784 * q^94 + 158926 * q^96 - 47800 * q^97 - 99900 * q^98

Decomposition of \(S_{6}^{\mathrm{new}}(200, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
200.6.d.a	$200$	$6$	200.d	8.b	$2$	$4$	$4$	$32.077$	4.0.218489.1	None					8.6.b.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(-96\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(5+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
200.6.d.b	$200$	$6$	200.d	8.b	$2$	$20$	$20$	$32.077$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None					40.6.d.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(196\)	$2^{45}\cdot 3^{4}\cdot 5^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(-2-\beta _{2})q^{4}+(10+\cdots)q^{6}+\cdots\)
200.6.d.c	$200$	$6$	200.d	8.b	$2$	$20$	$20$	$32.077$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓			200.6.d.c	$2$	$0$	\(-1\)	\(0\)	\(0\)	\(-196\)	$2^{49}\cdot 5^{4}\cdot 31$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-\beta _{5}q^{3}+\beta _{2}q^{4}+(2-\beta _{7}+\cdots)q^{6}+\cdots\)
200.6.d.d	$200$	$6$	200.d	8.b	$2$	$20$	$20$	$32.077$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓			200.6.d.c	$2$	$0$	\(1\)	\(0\)	\(0\)	\(196\)	$2^{49}\cdot 5^{4}\cdot 31$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+\beta _{6}q^{3}-\beta _{2}q^{4}+(2-\beta _{10}+\cdots)q^{6}+\cdots\)
200.6.d.e	$200$	$6$	200.d	8.b	$2$	$28$	$28$	$32.077$		None			✓		40.6.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{6}^{\mathrm{old}}(200, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(200, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)