Space of modular forms of level 99, weight 6, and Character 99.g

• Label: 99.6.g
• Level: $99$
• Weight: $6$
• Character orbit: 99.g
• Rep. character: $\chi_{99}(32,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $116$
• Newform subspaces: $2$
• Sturm bound: $72$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	99.g (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 99 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(72\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(99, [\chi])\).

	Total	New	Old
Modular forms	124	124	0
Cusp forms	116	116	0
Eisenstein series	8	8	0

Trace form

\( 116 q + 17 q^{3} - 898 q^{4} + 81 q^{5} + 401 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(99, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
99.6.g.a	$99$	$6$	99.g	99.g	$6$	$4$	$2$	$15.878$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	\(\Q(\sqrt{-11}) \)		$4$	$0$	\(0\)	\(-31\)	\(171\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-15\beta _{2}+\beta _{3})q^{3}+2^{5}\beta _{2}q^{4}+(57+\cdots)q^{5}+\cdots\)
99.6.g.b	$99$	$6$	99.g	99.g	$6$	$112$	$56$	$15.878$		None		$4$	$0$	\(0\)	\(48\)	\(-90\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$