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

• Label: 200.3.e
• Level: $200$
• Weight: $3$
• Character orbit: 200.e
• Rep. character: $\chi_{200}(99,\cdot)$
• Character field: $\Q$
• Dimension: $34$
• Newform subspaces: $4$
• Sturm bound: $90$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	200.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(90\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	66	38	28
Cusp forms	54	34	20
Eisenstein series	12	4	8

Trace form

34 * q + 6 * q^4 - 22 * q^6 - 86 * q^9 - 4 * q^11 + 32 * q^14 + 34 * q^16 - 60 * q^19 - 102 * q^24 + 48 * q^26 - 202 * q^34 - 88 * q^36 - 44 * q^41 + 330 * q^44 + 88 * q^46 + 158 * q^49 - 232 * q^51 + 578 * q^54 + 208 * q^56 + 132 * q^59 - 354 * q^64 - 162 * q^66 - 528 * q^74 - 74 * q^76 + 90 * q^81 + 880 * q^84 - 620 * q^86 - 100 * q^89 + 576 * q^91 + 832 * q^94 + 78 * q^96 + 108 * q^99

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.e.a	$200$	$3$	200.e	40.e	$2$	$2$	$2$	$5.450$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-2}) \)					8.3.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{2}-\beta q^{3}-4 q^{4}+4 q^{6}-4\beta q^{8}+\cdots\)
200.3.e.b	$200$	$3$	200.e	40.e	$2$	$4$	$4$	$5.450$	\(\Q(i, \sqrt{6})\)	\(\Q(\sqrt{-2}) \)		✓			200.3.g.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q+2\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}-4q^{4}+(-2+\cdots)q^{6}+\cdots\)
200.3.e.c	$200$	$3$	200.e	40.e	$2$	$12$	$12$	$5.450$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			200.3.g.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{6}+\beta _{9})q^{4}+\cdots\)
200.3.e.d	$200$	$3$	200.e	40.e	$2$	$16$	$16$	$5.450$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None			✓		40.3.g.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{27}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+\beta _{2}q^{3}+(1+\beta _{11})q^{4}+(-2+\cdots)q^{6}+\cdots\)

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

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