Space of modular forms of level 200, weight 5, and Character 200.l

• Label: 200.5.l
• Level: $200$
• Weight: $5$
• Character orbit: 200.l
• Rep. character: $\chi_{200}(57,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $36$
• Newform subspaces: $7$
• Sturm bound: $150$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	200.l (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(150\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(200, [\chi])\).

	Total	New	Old
Modular forms	264	36	228
Cusp forms	216	36	180
Eisenstein series	48	0	48

Trace form

36 * q + 80 * q^7 - 288 * q^11 - 20 * q^13 + 60 * q^17 + 416 * q^21 + 1920 * q^23 + 240 * q^27 - 1856 * q^31 - 4560 * q^33 - 3580 * q^37 + 8256 * q^41 + 2400 * q^43 + 8640 * q^47 - 12240 * q^51 - 12060 * q^53 - 14560 * q^57 + 8496 * q^61 + 32320 * q^63 + 17600 * q^67 - 5568 * q^71 - 27500 * q^73 - 10320 * q^77 + 1244 * q^81 + 36240 * q^83 + 8960 * q^87 - 12032 * q^91 - 53040 * q^93 - 22060 * q^97

Decomposition of \(S_{5}^{\mathrm{new}}(200, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
200.5.l.a	$200$	$5$	200.l	5.c	$4$	$2$	$1$	$20.674$	\(\Q(\sqrt{-1}) \)	None					40.5.l.a	$2$	$0$	\(0\)	\(-20\)	\(0\)	\(84\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(10 i-10)q^{3}+(42 i+42)q^{7}+\cdots\)
200.5.l.b	$200$	$5$	200.l	5.c	$4$	$4$	$2$	$20.674$	\(\Q(i, \sqrt{61})\)	None		✓			200.5.l.b	$2$	$0$	\(0\)	\(-16\)	\(0\)	\(48\)	$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-4+4\beta _{1}-\beta _{3})q^{3}+(12+12\beta _{1}+\cdots)q^{7}+\cdots\)
200.5.l.c	$200$	$5$	200.l	5.c	$4$	$4$	$2$	$20.674$	\(\Q(i, \sqrt{29})\)	None					40.5.l.b	$2$	$0$	\(0\)	\(12\)	\(0\)	\(-44\)	$2^{5}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(3-3\beta _{1})q^{3}+(-11-11\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
200.5.l.d	$200$	$5$	200.l	5.c	$4$	$4$	$2$	$20.674$	\(\Q(i, \sqrt{61})\)	None		✓			200.5.l.b	$2$	$0$	\(0\)	\(16\)	\(0\)	\(-48\)	$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(4+4\beta _{1}-\beta _{2})q^{3}+(-12+12\beta _{1}+\cdots)q^{7}+\cdots\)
200.5.l.e	$200$	$5$	200.l	5.c	$4$	$6$	$3$	$20.674$	6.0.313431616.3	None					40.5.l.c	$2$	$0$	\(0\)	\(8\)	\(0\)	\(40\)	$2^{6}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\beta _{1}+\beta _{3})q^{3}+(6-6\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)
200.5.l.f	$200$	$5$	200.l	5.c	$4$	$8$	$4$	$20.674$	8.0.\(\cdots\).18	None		✓			200.5.l.f	$2$	$0$	\(0\)	\(-8\)	\(0\)	\(-48\)	$2^{6}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-\beta _{1}+\beta _{3})q^{3}+(-6+6\beta _{1}+\cdots)q^{7}+\cdots\)
200.5.l.g	$200$	$5$	200.l	5.c	$4$	$8$	$4$	$20.674$	8.0.\(\cdots\).18	None		✓			200.5.l.f	$2$	$0$	\(0\)	\(8\)	\(0\)	\(48\)	$2^{6}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-\beta _{1}-\beta _{2})q^{3}+(6+6\beta _{1}-2\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(200, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(200, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)