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

• Label: 200.4.c
• Level: $200$
• Weight: $4$
• Character orbit: 200.c
• Rep. character: $\chi_{200}(49,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $7$
• Sturm bound: $120$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	200.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(120\)
Trace bound:			\(11\)
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	102	14	88
Cusp forms	78	14	64
Eisenstein series	24	0	24

Trace form

\( 14 q - 172 q^{9} + O(q^{10}) \)

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.c.a	$200$	$4$	200.c	5.b	$2$	$2$	$2$	$11.800$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+5iq^{3}+9iq^{7}-73q^{9}-2^{4}q^{11}+\cdots\)
200.4.c.b	$200$	$4$	200.c	5.b	$2$	$2$	$2$	$11.800$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+9iq^{3}-26iq^{7}-54q^{9}-59q^{11}+\cdots\)
200.4.c.c	$200$	$4$	200.c	5.b	$2$	$2$	$2$	$11.800$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}-17iq^{7}-9q^{9}+2^{4}q^{11}+\cdots\)
200.4.c.d	$200$	$4$	200.c	5.b	$2$	$2$	$2$	$11.800$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+5iq^{3}-2iq^{7}+2q^{9}+39q^{11}+\cdots\)
200.4.c.e	$200$	$4$	200.c	5.b	$2$	$2$	$2$	$11.800$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}+12iq^{7}+11q^{9}-44q^{11}+\cdots\)
200.4.c.f	$200$	$4$	200.c	5.b	$2$	$2$	$2$	$11.800$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}-8iq^{7}+11q^{9}+6^{2}q^{11}+\cdots\)
200.4.c.g	$200$	$4$	200.c	5.b	$2$	$2$	$2$	$11.800$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+6iq^{7}+26q^{9}-19q^{11}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(200, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)