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

• Label: 200.3.n
• Level: $200$
• Weight: $3$
• Character orbit: 200.n
• Rep. character: $\chi_{200}(11,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $232$
• 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.n (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 200 \)
Character field:			\(\Q(\zeta_{10})\)
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	248	248	0
Cusp forms	232	232	0
Eisenstein series	16	16	0

Trace form

\( 232 q - 3 q^{2} - 6 q^{3} - 3 q^{4} + 5 q^{6} - 12 q^{8} - 168 q^{9} + O(q^{10}) \)

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.n.a	$200$	$3$	200.n	200.n	$10$	$232$	$58$	$5.450$		None		✓	✓	✓	200.3.n.a	$4$	$0$	\(-3\)	\(-6\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$