Space of modular forms of level 200, weight 3, and Character 200.l

• Label: 200.3.l
• Level: $200$
• Weight: $3$
• Character orbit: 200.l
• Rep. character: $\chi_{200}(57,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $18$
• Newform subspaces: $6$
• Sturm bound: $90$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	200.l (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(90\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(200, [\chi])\).

	Total	New	Old
Modular forms	144	18	126
Cusp forms	96	18	78
Eisenstein series	48	0	48

Trace form

18 * q - 8 * q^7 + 16 * q^11 + 38 * q^13 + 14 * q^17 - 112 * q^21 - 96 * q^23 - 120 * q^27 + 32 * q^31 + 120 * q^33 + 82 * q^37 + 128 * q^41 - 48 * q^43 + 128 * q^47 + 360 * q^51 + 66 * q^53 + 80 * q^57 - 312 * q^61 - 128 * q^63 - 224 * q^67 - 544 * q^71 - 166 * q^73 - 72 * q^77 - 178 * q^81 + 184 * q^83 + 320 * q^87 - 256 * q^91 - 120 * q^93 - 38 * q^97

Decomposition of \(S_{3}^{\mathrm{new}}(200, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
200.3.l.a	$200$	$3$	200.l	5.c	$4$	$2$	$1$	$5.450$	\(\Q(\sqrt{-1}) \)	None		✓			200.3.l.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-14\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i-1)q^{3}+(-7 i-7)q^{7}+7 i q^{9}+\cdots\)
200.3.l.b	$200$	$3$	200.l	5.c	$4$	$2$	$1$	$5.450$	\(\Q(\sqrt{-1}) \)	None					40.3.l.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i-1)q^{3}+(3 i+3)q^{7}+7 i q^{9}+\cdots\)
200.3.l.c	$200$	$3$	200.l	5.c	$4$	$2$	$1$	$5.450$	\(\Q(\sqrt{-1}) \)	None		✓			200.3.l.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(14\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i+1)q^{3}+(7 i+7)q^{7}+7 i q^{9}+\cdots\)
200.3.l.d	$200$	$3$	200.l	5.c	$4$	$4$	$2$	$5.450$	\(\Q(i, \sqrt{6})\)	None		✓			200.3.l.d	$2$	$0$	\(0\)	\(-8\)	\(0\)	\(16\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2+2\beta _{2}+\beta _{3})q^{3}+(4+4\beta _{1}+4\beta _{2}+\cdots)q^{7}+\cdots\)
200.3.l.e	$200$	$3$	200.l	5.c	$4$	$4$	$2$	$5.450$	\(\Q(i, \sqrt{41})\)	None					40.3.l.b	$2$	$0$	\(0\)	\(2\)	\(0\)	\(-14\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-\beta _{1}+\beta _{3})q^{3}+(-3-4\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
200.3.l.f	$200$	$3$	200.l	5.c	$4$	$4$	$2$	$5.450$	\(\Q(i, \sqrt{6})\)	None		✓			200.3.l.d	$2$	$0$	\(0\)	\(8\)	\(0\)	\(-16\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2-2\beta _{2}+\beta _{3})q^{3}+(-4+4\beta _{1}-4\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(200, [\chi])\) into lower level spaces

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