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

• Label: 99.2.j
• Level: $99$
• Weight: $2$
• Character orbit: 99.j
• Rep. character: $\chi_{99}(8,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.j (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(24\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	64	16	48
Cusp forms	32	16	16
Eisenstein series	32	0	32

Trace form

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

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.j.a	$99$	$2$	99.j	33.f	$10$	$16$	$4$	$0.791$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(\beta _{8}-\beta _{10}-\beta _{11}+\beta _{12}-\beta _{14}+2\beta _{15})q^{2}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(99, [\chi])\) into lower level spaces

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