Space of modular forms of level 200, weight 12, and Character 200.c

• Label: 200.12.c
• Level: $200$
• Weight: $12$
• Character orbit: 200.c
• Rep. character: $\chi_{200}(49,\cdot)$
• Character field: $\Q$
• Dimension: $50$
• Newform subspaces: $9$
• Sturm bound: $360$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	200.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(360\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(200, [\chi])\).

	Total	New	Old
Modular forms	342	50	292
Cusp forms	318	50	268
Eisenstein series	24	0	24

Trace form

50 * q - 3125104 * q^9 - 308062 * q^11 + 8361838 * q^19 - 42310484 * q^21 - 213782984 * q^29 + 342797492 * q^31 + 3504195032 * q^39 + 590874262 * q^41 - 23170394058 * q^49 + 1946263170 * q^51 + 20750633168 * q^59 - 15856522732 * q^61 - 23887002116 * q^69 - 36962103768 * q^71 - 142297582476 * q^79 + 105893451010 * q^81 + 75109332078 * q^89 - 55845785600 * q^91 + 89854048292 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(200, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
200.12.c.a	$200$	$12$	200.c	5.b	$2$	$2$	$2$	$153.669$	\(\Q(\sqrt{-1}) \)	None					40.12.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+260\beta q^{3}-7574\beta q^{7}-93253 q^{9}+\cdots\)
200.12.c.b	$200$	$12$	200.c	5.b	$2$	$2$	$2$	$153.669$	\(\Q(\sqrt{-1}) \)	None					8.12.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+18\beta q^{3}-27732\beta q^{7}+175851 q^{9}+\cdots\)
200.12.c.c	$200$	$12$	200.c	5.b	$2$	$4$	$4$	$153.669$	\(\Q(i, \sqrt{109})\)	None					8.12.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-14\beta _{1}+\beta _{2})q^{3}+(22764\beta _{1}-42\beta _{2}+\cdots)q^{7}+\cdots\)
200.12.c.d	$200$	$12$	200.c	5.b	$2$	$4$	$4$	$153.669$	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None					40.12.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{15}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-198\beta _{1}q^{3}+(-1408\beta _{1}-\beta _{2})q^{7}+\cdots\)
200.12.c.e	$200$	$12$	200.c	5.b	$2$	$4$	$4$	$153.669$	\(\Q(i, \sqrt{57})\)	None					40.12.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(63\beta _{1}-\beta _{2})q^{3}+(6053\beta _{1}-65\beta _{2}+\cdots)q^{7}+\cdots\)
200.12.c.f	$200$	$12$	200.c	5.b	$2$	$6$	$6$	$153.669$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None					40.12.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{24}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(13\beta _{1}-\beta _{3})q^{3}+(-255\beta _{1}-5^{2}\beta _{3}+\cdots)q^{7}+\cdots\)
200.12.c.g	$200$	$12$	200.c	5.b	$2$	$6$	$6$	$153.669$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None					40.12.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{24}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2^{4}\beta _{1}-\beta _{3})q^{3}+(-16815\beta _{1}-3^{3}\beta _{3}+\cdots)q^{7}+\cdots\)
200.12.c.h	$200$	$12$	200.c	5.b	$2$	$10$	$10$	$153.669$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓			200.12.a.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{32}\cdot 3^{2}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-51\beta _{4})q^{3}+(-46\beta _{1}+707\beta _{4}+\cdots)q^{7}+\cdots\)
200.12.c.i	$200$	$12$	200.c	5.b	$2$	$12$	$12$	$153.669$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓	✓		200.12.a.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{48}\cdot 3^{2}\cdot 5^{10}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+83\beta _{7})q^{3}+(-5^{2}\beta _{1}-7962\beta _{7}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(200, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(200, [\chi]) \simeq \) \(S_{12}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)