Space of modular forms of level 99, weight 9, and Character 99.c

• Label: 99.9.c
• Level: $99$
• Weight: $9$
• Character orbit: 99.c
• Rep. character: $\chi_{99}(10,\cdot)$
• Character field: $\Q$
• Dimension: $39$
• Newform subspaces: $4$
• Sturm bound: $108$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	99.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(108\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(99, [\chi])\).

	Total	New	Old
Modular forms	100	41	59
Cusp forms	92	39	53
Eisenstein series	8	2	6

Trace form

\( 39 q - 5052 q^{4} + 413 q^{5} + O(q^{10}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(99, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
99.9.c.a	$99$	$9$	99.c	11.b	$2$	$1$	$1$	$40.330$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(-1151\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{8}q^{4}-1151q^{5}-11^{4}q^{11}+2^{16}q^{16}+\cdots\)
99.9.c.b	$99$	$9$	99.c	11.b	$2$	$6$	$6$	$40.330$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(448\)	\(0\)	$2^{7}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-203+3\beta _{3}-2\beta _{4})q^{4}+\cdots\)
99.9.c.c	$99$	$9$	99.c	11.b	$2$	$16$	$16$	$40.330$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{20}\cdot 3^{14}\cdot 11^{5}\cdot 29^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(-151-\beta _{1})q^{4}+\beta _{3}q^{5}+\cdots\)
99.9.c.d	$99$	$9$	99.c	11.b	$2$	$16$	$16$	$40.330$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(1116\)	\(0\)	$2^{13}\cdot 3^{23}\cdot 11^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-105+\beta _{2})q^{4}+(70-\beta _{4}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(99, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(99, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)