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 - 94 * q^11 + 46 * q^19 + 460 * q^21 - 368 * q^29 - 492 * q^31 - 40 * q^39 + 1246 * q^41 - 1254 * q^49 - 1230 * q^51 + 704 * q^59 + 572 * q^61 + 700 * q^69 - 2520 * q^71 + 500 * q^79 + 3646 * q^81 + 966 * q^89 - 2368 * q^91 + 7412 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
200.4.c.a	$200$	$4$	200.c	5.b	$2$	$2$	$2$	$11.800$	\(\Q(\sqrt{-1}) \)	None					40.4.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+5\beta q^{3}+9\beta q^{7}-73 q^{9}-16 q^{11}+\cdots\)
200.4.c.b	$200$	$4$	200.c	5.b	$2$	$2$	$2$	$11.800$	\(\Q(\sqrt{-1}) \)	None		✓			200.4.a.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+9 i q^{3}-26 i q^{7}-54 q^{9}-59 q^{11}+\cdots\)
200.4.c.c	$200$	$4$	200.c	5.b	$2$	$2$	$2$	$11.800$	\(\Q(\sqrt{-1}) \)	None					40.4.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+3\beta q^{3}-17\beta q^{7}-9 q^{9}+16 q^{11}+\cdots\)
200.4.c.d	$200$	$4$	200.c	5.b	$2$	$2$	$2$	$11.800$	\(\Q(\sqrt{-1}) \)	None		✓			200.4.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+5 i q^{3}-2 i q^{7}+2 q^{9}+39 q^{11}+\cdots\)
200.4.c.e	$200$	$4$	200.c	5.b	$2$	$2$	$2$	$11.800$	\(\Q(\sqrt{-1}) \)	None					8.4.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{3}+12\beta q^{7}+11 q^{9}-44 q^{11}+\cdots\)
200.4.c.f	$200$	$4$	200.c	5.b	$2$	$2$	$2$	$11.800$	\(\Q(\sqrt{-1}) \)	None					40.4.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{3}-8\beta q^{7}+11 q^{9}+36 q^{11}+\cdots\)
200.4.c.g	$200$	$4$	200.c	5.b	$2$	$2$	$2$	$11.800$	\(\Q(\sqrt{-1}) \)	None		✓			200.4.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+6 i q^{7}+26 q^{9}-19 q^{11}+\cdots\)

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

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