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

• Label: 99.6.d
• Level: $99$
• Weight: $6$
• Character orbit: 99.d
• Rep. character: $\chi_{99}(98,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $72$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	99.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(72\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	64	20	44
Cusp forms	56	20	36
Eisenstein series	8	0	8

Trace form

\( 20 q + 320 q^{4} + O(q^{10}) \)

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.d.a	$99$	$6$	99.d	33.d	$2$	$20$	$20$	$15.878$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{25}\cdot 3^{26}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{10}q^{2}+(2^{4}+\beta _{1})q^{4}-\beta _{11}q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(99, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(99, [\chi]) \cong \)