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

• Label: 99.6.e
• Level: $99$
• Weight: $6$
• Character orbit: 99.e
• Rep. character: $\chi_{99}(34,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $100$
• 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.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
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	100	24
Cusp forms	116	100	16
Eisenstein series	8	0	8

Trace form

\( 100 q - q^{3} - 800 q^{4} - 129 q^{5} - 274 q^{6} - 58 q^{7} + 852 q^{8} + 349 q^{9} + O(q^{10}) \)

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.e.a	$99$	$6$	99.e	9.c	$3$	$46$	$23$	$15.878$		None		$2$	$0$	\(0\)	\(15\)	\(-36\)	\(167\)		$\mathrm{SU}(2)[C_{3}]$
99.6.e.b	$99$	$6$	99.e	9.c	$3$	$54$	$27$	$15.878$		None		$2$	$0$	\(0\)	\(-16\)	\(-93\)	\(-225\)		$\mathrm{SU}(2)[C_{3}]$

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

\( S_{6}^{\mathrm{old}}(99, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)