Space of modular forms of level 99, weight 2, and Character 99.g

• Label: 99.2.g
• Level: $99$
• Weight: $2$
• Character orbit: 99.g
• Rep. character: $\chi_{99}(32,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $20$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(24\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(99, [\chi])\).

	Total	New	Old
Modular forms	28	28	0
Cusp forms	20	20	0
Eisenstein series	8	8	0

Trace form

\( 20 q - 7 q^{3} - 10 q^{4} - 9 q^{5} + 11 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(99, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
99.2.g.a	$99$	$2$	99.g	99.g	$6$	$4$	$2$	$0.791$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	\(\Q(\sqrt{-11}) \)		$4$	$0$	\(0\)	\(-1\)	\(-9\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q-\beta _{1}q^{3}+(2-2\beta _{2})q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
99.2.g.b	$99$	$2$	99.g	99.g	$6$	$16$	$8$	$0.791$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(\beta _{6}-\beta _{7}+\beta _{9}+\beta _{12}+\beta _{13}+\cdots)q^{3}+\cdots\)