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

• Label: 99.6.m
• Level: $99$
• Weight: $6$
• Character orbit: 99.m
• Rep. character: $\chi_{99}(4,\cdot)$
• Character field: $\Q(\zeta_{15})$
• Dimension: $464$
• 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.m (of order \(15\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 99 \)
Character field:			\(\Q(\zeta_{15})\)
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	496	496	0
Cusp forms	464	464	0
Eisenstein series	32	32	0

Trace form

\( 464 q - 11 q^{2} + 15 q^{3} + 893 q^{4} - 32 q^{5} - 58 q^{6} - 3 q^{7} + 628 q^{8} - 631 q^{9} + O(q^{10}) \)

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.m.a	$99$	$6$	99.m	99.m	$15$	$464$	$58$	$15.878$		None		$4$	$0$	\(-11\)	\(15\)	\(-32\)	\(-3\)		$\mathrm{SU}(2)[C_{15}]$