Space of modular forms of level 200, weight 2, and Character 200.d

• Label: 200.2.d
• Level: $200$
• Weight: $2$
• Character orbit: 200.d
• Rep. character: $\chi_{200}(101,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $6$
• Sturm bound: $60$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	200.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(60\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(200, [\chi])\).

	Total	New	Old
Modular forms	36	22	14
Cusp forms	24	16	8
Eisenstein series	12	6	6

Trace form

16 * q + 2 * q^2 - 2 * q^4 - 10 * q^6 + 4 * q^7 + 8 * q^8 - 8 * q^9 + 4 * q^12 - 14 * q^16 - 14 * q^18 - 4 * q^22 + 4 * q^23 + 14 * q^24 + 12 * q^26 - 12 * q^28 - 8 * q^31 - 8 * q^32 - 8 * q^33 - 6 * q^34 + 4 * q^36 + 20 * q^38 + 4 * q^42 + 6 * q^44 - 20 * q^47 + 24 * q^48 + 8 * q^49 + 26 * q^54 - 48 * q^56 - 8 * q^57 - 24 * q^58 - 16 * q^62 + 20 * q^63 - 14 * q^64 + 42 * q^66 - 24 * q^68 - 8 * q^72 - 16 * q^73 - 36 * q^74 + 30 * q^76 + 24 * q^78 + 40 * q^79 - 32 * q^81 + 8 * q^82 - 24 * q^84 - 12 * q^86 + 48 * q^87 + 16 * q^88 + 36 * q^92 - 48 * q^94 + 14 * q^96 + 16 * q^97 - 18 * q^98

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.d.a	$200$	$2$	200.d	8.b	$2$	$2$	$2$	$1.597$	\(\Q(\sqrt{-1}) \)	None		✓			200.2.d.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(i-1)q^{2}-i q^{3}-2 i q^{4}+(i+1)q^{6}+\cdots\)
200.2.d.b	$200$	$2$	200.d	8.b	$2$	$2$	$2$	$1.597$	\(\Q(\sqrt{-7}) \)	None		✓			200.2.d.b	$2$	$0$	\(-1\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{2}+(1-2\beta )q^{3}+(-2+\beta )q^{4}+\cdots\)
200.2.d.c	$200$	$2$	200.d	8.b	$2$	$2$	$2$	$1.597$	\(\Q(\sqrt{-7}) \)	None		✓			200.2.d.b	$2$	$0$	\(1\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+(-1+2\beta )q^{3}+(-2+\beta )q^{4}+\cdots\)
200.2.d.d	$200$	$2$	200.d	8.b	$2$	$2$	$2$	$1.597$	\(\Q(\sqrt{-1}) \)	None		✓			200.2.d.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(i+1)q^{2}-i q^{3}+2 i q^{4}+(-i+1)q^{6}+\cdots\)
200.2.d.e	$200$	$2$	200.d	8.b	$2$	$4$	$4$	$1.597$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None					40.2.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(1+\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots\)
200.2.d.f	$200$	$2$	200.d	8.b	$2$	$4$	$4$	$1.597$	\(\Q(\zeta_{12})\)	None					40.2.d.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta_{2}+\beta_1)q^{2}+(\beta_{3}-\beta_{2}-\beta_1+1)q^{3}+\cdots\)

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

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