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 + 10 * q^11 - 10 * q^19 - 12 * q^21 + 20 * q^29 + 4 * q^31 + 24 * q^39 - 18 * q^41 - 12 * q^49 - 30 * q^51 - 8 * q^59 + 16 * q^61 - 12 * q^69 - 24 * q^71 - 12 * q^79 + 36 * q^81 + 30 * q^89 + 32 * q^91 + 12 * q^99

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.c.a	$200$	$2$	200.c	5.b	$2$	$2$	$2$	$1.597$	\(\Q(\sqrt{-1}) \)	None		✓			200.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{3}+2 i q^{7}-6 q^{9}+q^{11}+\cdots\)
200.2.c.b	$200$	$2$	200.c	5.b	$2$	$2$	$2$	$1.597$	\(\Q(\sqrt{-1}) \)	None					40.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{7}+3 q^{9}+4 q^{11}-\beta q^{13}+\cdots\)

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

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