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

• Label: 99.2.d
• Level: $99$
• Weight: $2$
• Character orbit: 99.d
• Rep. character: $\chi_{99}(98,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• 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.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
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	16	4	12
Cusp forms	8	4	4
Eisenstein series	8	0	8

Trace form

\( 4 q + 4 q^{4} - 20 q^{16} - 12 q^{22} + 12 q^{25} - 16 q^{31} + 32 q^{37} + 4 q^{49} - 16 q^{55} + 48 q^{58} + 4 q^{64} - 16 q^{67} + 24 q^{70} - 48 q^{82} + 12 q^{88} - 48 q^{91} - 40 q^{97}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
99.2.d.a	$99$	$2$	99.d	33.d	$2$	$4$	$4$	$0.791$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		✓	✓	✓	99.2.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+q^{4}-\beta _{1}q^{5}-\beta _{3}q^{7}+\beta _{2}q^{8}+\cdots\)

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

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