Space of modular forms of level 200, weight 8, and Character 200.c

• Label: 200.8.c
• Level: $200$
• Weight: $8$
• Character orbit: 200.c
• Rep. character: $\chi_{200}(49,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $10$
• Sturm bound: $240$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	200.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(240\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(200, [\chi])\).

	Total	New	Old
Modular forms	222	32	190
Cusp forms	198	32	166
Eisenstein series	24	0	24

Trace form

\( 32 q - 23278 q^{9} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(200, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
200.8.c.a	$200$	$8$	200.c	5.b	$2$	$2$	$2$	$62.477$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+42iq^{3}-228iq^{7}-4869q^{9}-2524q^{11}+\cdots\)
200.8.c.b	$200$	$8$	200.c	5.b	$2$	$2$	$2$	$62.477$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+69iq^{3}+174iq^{7}-2574q^{9}+7111q^{11}+\cdots\)
200.8.c.c	$200$	$8$	200.c	5.b	$2$	$2$	$2$	$62.477$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+22iq^{3}+612iq^{7}+251q^{9}-3164q^{11}+\cdots\)
200.8.c.d	$200$	$8$	200.c	5.b	$2$	$2$	$2$	$62.477$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+18iq^{3}+388iq^{7}+891q^{9}-124q^{11}+\cdots\)
200.8.c.e	$200$	$8$	200.c	5.b	$2$	$2$	$2$	$62.477$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+9iq^{3}+694iq^{7}+2106q^{9}+4901q^{11}+\cdots\)
200.8.c.f	$200$	$8$	200.c	5.b	$2$	$4$	$4$	$62.477$	\(\Q(i, \sqrt{3889})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2\beta _{1}-\beta _{2})q^{3}+(-572\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots\)
200.8.c.g	$200$	$8$	200.c	5.b	$2$	$4$	$4$	$62.477$	\(\Q(i, \sqrt{601})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-19\beta _{1}+\beta _{2})q^{3}+(199\beta _{1}-7\beta _{2}+\cdots)q^{7}+\cdots\)
200.8.c.h	$200$	$8$	200.c	5.b	$2$	$4$	$4$	$62.477$	\(\Q(i, \sqrt{46})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{2})q^{3}+(-211\beta _{1}-17\beta _{2}+\cdots)q^{7}+\cdots\)
200.8.c.i	$200$	$8$	200.c	5.b	$2$	$4$	$4$	$62.477$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(9\beta _{1}+\beta _{2})q^{3}+(101\beta _{1}+63\beta _{2})q^{7}+\cdots\)
200.8.c.j	$200$	$8$	200.c	5.b	$2$	$6$	$6$	$62.477$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2^{5}\beta _{1}+\beta _{2})q^{3}+(-543\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(200, [\chi])\) into lower level spaces

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