Space of modular forms of level 99, weight 3, and Character 99.o

• Label: 99.3.o
• Level: $99$
• Weight: $3$
• Character orbit: 99.o
• Rep. character: $\chi_{99}(7,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $176$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	99.o (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 99 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(36\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(99, [\chi])\).

	Total	New	Old
Modular forms	208	208	0
Cusp forms	176	176	0
Eisenstein series	32	32	0

Trace form

\( 176 q - 5 q^{2} - 9 q^{3} - 43 q^{4} - 6 q^{5} - 30 q^{6} - 5 q^{7} - 20 q^{8} + 23 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(99, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
99.3.o.a	$99$	$3$	99.o	99.o	$30$	$176$	$22$	$2.698$		None		$4$	$0$	\(-5\)	\(-9\)	\(-6\)	\(-5\)		$\mathrm{SU}(2)[C_{30}]$