Space of modular forms of level 99, weight 3, and Character 99.l

• Label: 99.3.l
• Level: $99$
• Weight: $3$
• Character orbit: 99.l
• Rep. character: $\chi_{99}(26,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $32$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	99.l (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(36\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(99, [\chi])\).

	Total	New	Old
Modular forms	112	32	80
Cusp forms	80	32	48
Eisenstein series	32	0	32

Trace form

\( 32 q + 16 q^{4} - 16 q^{7} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(99, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
99.3.l.a	$99$	$3$	99.l	33.h	$10$	$32$	$8$	$2.698$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{3}^{\mathrm{old}}(99, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(99, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)