Space of modular forms of level 200, weight 4, and Character 200.d

• Label: 200.4.d
• Level: $200$
• Weight: $4$
• Character orbit: 200.d
• Rep. character: $\chi_{200}(101,\cdot)$
• Character field: $\Q$
• Dimension: $54$
• Newform subspaces: $5$
• Sturm bound: $120$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(120\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(200, [\chi])\).

	Total	New	Old
Modular forms	96	60	36
Cusp forms	84	54	30
Eisenstein series	12	6	6

Trace form

\( 54 q + 2 q^{4} - 2 q^{6} - 12 q^{7} - 430 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(200, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
200.4.d.a	$200$	$4$	200.d	8.b	$2$	$2$	$2$	$11.800$	\(\Q(\sqrt{-7}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(16\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta )q^{2}-2\beta q^{3}+(-6+2\beta )q^{4}+\cdots\)
200.4.d.b	$200$	$4$	200.d	8.b	$2$	$12$	$12$	$11.800$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-28\)	$2^{15}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{6})q^{4}+(-3+\cdots)q^{6}+\cdots\)
200.4.d.c	$200$	$4$	200.d	8.b	$2$	$12$	$12$	$11.800$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(-1\)	\(0\)	\(0\)	\(28\)	$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{2}-\beta _{2}q^{3}+\beta _{3}q^{4}+(1+\beta _{2}+\cdots)q^{6}+\cdots\)
200.4.d.d	$200$	$4$	200.d	8.b	$2$	$12$	$12$	$11.800$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(1\)	\(0\)	\(0\)	\(-28\)	$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{4}q^{3}+\beta _{2}q^{4}+(1-\beta _{4}+\cdots)q^{6}+\cdots\)
200.4.d.e	$200$	$4$	200.d	8.b	$2$	$16$	$16$	$11.800$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{21}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{12}q^{3}+\beta _{2}q^{4}+(-1-\beta _{7}+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(200, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(200, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)