Space of modular forms of level 200, weight 2, and Character 200.v

• Label: 200.2.v
• Level: $200$
• Weight: $2$
• Character orbit: 200.v
• Rep. character: $\chi_{200}(3,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $224$
• Newform subspaces: $3$
• Sturm bound: $60$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	200.v (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 200 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(60\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(200, [\chi])\).

	Total	New	Old
Modular forms	256	256	0
Cusp forms	224	224	0
Eisenstein series	32	32	0

Trace form

224 * q - 8 * q^2 - 16 * q^3 - 10 * q^4 - 6 * q^6 - 14 * q^8 - 20 * q^9 - 12 * q^11 - 22 * q^12 - 10 * q^14 - 6 * q^16 - 12 * q^17 - 20 * q^18 - 20 * q^19 - 10 * q^20 - 22 * q^22 - 20 * q^25 - 16 * q^26 - 28 * q^27 + 10 * q^28 - 30 * q^30 + 22 * q^32 - 4 * q^33 - 10 * q^34 - 40 * q^35 - 22 * q^36 - 36 * q^38 + 60 * q^40 - 12 * q^41 - 90 * q^42 - 48 * q^43 + 60 * q^44 - 6 * q^46 + 104 * q^48 - 90 * q^50 - 32 * q^51 + 60 * q^52 - 140 * q^54 - 6 * q^56 - 28 * q^57 - 100 * q^58 - 20 * q^59 + 70 * q^60 - 100 * q^62 + 20 * q^64 - 20 * q^65 + 18 * q^66 + 8 * q^67 - 6 * q^68 - 30 * q^70 + 40 * q^72 - 36 * q^73 + 40 * q^75 - 32 * q^76 - 10 * q^80 + 12 * q^81 + 58 * q^82 + 24 * q^83 + 70 * q^84 - 6 * q^86 + 94 * q^88 - 120 * q^89 + 150 * q^90 - 12 * q^91 + 70 * q^92 + 150 * q^94 - 26 * q^96 + 44 * q^97 + 156 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(200, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
200.2.v.a	$200$	$2$	200.v	200.v	$20$	$8$	$1$	$1.597$	\(\Q(\zeta_{20})\)	None		✓			200.2.v.a	$2$	$0$	\(-8\)	\(0\)	\(10\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{20}]$	\(q+(-1+\zeta_{20}^{5})q^{2}+(1-\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{3}+\cdots\)
200.2.v.b	$200$	$2$	200.v	200.v	$20$	$8$	$1$	$1.597$	\(\Q(\zeta_{20})\)	None		✓			200.2.v.a	$2$	$0$	\(-2\)	\(0\)	\(-10\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{20}]$	\(q+(-\zeta_{20}-\zeta_{20}^{6})q^{2}+(1-\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{3}+\cdots\)
200.2.v.c	$200$	$2$	200.v	200.v	$20$	$208$	$26$	$1.597$		None		✓	✓		200.2.v.c	$4$	$0$	\(2\)	\(-16\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$