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

• Label: 200.2.c
• Level: $200$
• Weight: $2$
• Character orbit: 200.c
• Rep. character: $\chi_{200}(49,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $60$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	200.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(60\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	42	4	38
Cusp forms	18	4	14
Eisenstein series	24	0	24

Trace form

\( 4 q - 6 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
200.2.c.a	$200$	$2$	200.c	5.b	$2$	$2$	$2$	$1.597$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}+2iq^{7}-6q^{9}+q^{11}-4iq^{13}+\cdots\)
200.2.c.b	$200$	$2$	200.c	5.b	$2$	$2$	$2$	$1.597$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{7}+3q^{9}+4q^{11}-iq^{13}-iq^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(200, [\chi])\) into lower level spaces

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