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

• Label: 200.2.f
• Level: $200$
• Weight: $2$
• Character orbit: 200.f
• Rep. character: $\chi_{200}(149,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $5$
• Sturm bound: $60$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	200.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(60\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	36	20	16
Cusp forms	24	16	8
Eisenstein series	12	4	8

Trace form

16 * q + 6 * q^4 - 2 * q^6 + 16 * q^9 - 8 * q^14 + 2 * q^16 - 38 * q^24 - 32 * q^31 + 42 * q^34 - 24 * q^36 - 24 * q^39 - 8 * q^41 + 10 * q^44 + 32 * q^46 - 50 * q^54 - 40 * q^56 - 18 * q^64 + 2 * q^66 + 56 * q^71 + 56 * q^74 - 10 * q^76 + 8 * q^79 - 8 * q^81 + 56 * q^84 - 4 * q^86 - 32 * q^89 + 16 * q^94 + 62 * q^96

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.f.a	$200$	$2$	200.f	40.f	$2$	$2$	$2$	$1.597$	\(\Q(\sqrt{-1}) \)	None		✓			200.2.d.a	$2$	$0$	\(-2\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(i-1)q^{2}-q^{3}-2 i q^{4}+(-i+1)q^{6}+\cdots\)
200.2.f.b	$200$	$2$	200.f	40.f	$2$	$2$	$2$	$1.597$	\(\Q(\sqrt{-1}) \)	None		✓			200.2.d.a	$2$	$0$	\(2\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(i+1)q^{2}+q^{3}+2 i q^{4}+(i+1)q^{6}+\cdots\)
200.2.f.c	$200$	$2$	200.f	40.f	$2$	$4$	$4$	$1.597$	\(\Q(\zeta_{12})\)	None					40.2.d.a	$2$	$0$	\(-2\)	\(4\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{2}-\beta_1)q^{2}+(-\beta_{3}+\beta_{2}-\beta_1+1)q^{3}+\cdots\)
200.2.f.d	$200$	$2$	200.f	40.f	$2$	$4$	$4$	$1.597$	\(\Q(i, \sqrt{7})\)	None		✓			200.2.d.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
200.2.f.e	$200$	$2$	200.f	40.f	$2$	$4$	$4$	$1.597$	\(\Q(\zeta_{12})\)	None					40.2.d.a	$2$	$0$	\(2\)	\(-4\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta_{2}+\beta_1)q^{2}+(\beta_{3}-\beta_{2}+\beta_1-1)q^{3}+\cdots\)

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

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