Space of modular forms of level 99, weight 4, and Character 99.d

• Label: 99.4.d
• Level: $99$
• Weight: $4$
• Character orbit: 99.d
• Rep. character: $\chi_{99}(98,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $3$
• Sturm bound: $48$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	99.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(48\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(99, [\chi])\).

	Total	New	Old
Modular forms	40	12	28
Cusp forms	32	12	20
Eisenstein series	8	0	8

Trace form

\( 12 q + 48 q^{4} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(99, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
99.4.d.a	$99$	$4$	99.d	33.d	$2$	$2$	$2$	$5.841$	\(\Q(\sqrt{-2}) \)	None		$2$	$1$	\(-6\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-3q^{2}+q^{4}+14\beta q^{5}-12\beta q^{7}+21q^{8}+\cdots\)
99.4.d.b	$99$	$4$	99.d	33.d	$2$	$2$	$2$	$5.841$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(6\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3q^{2}+q^{4}+14\beta q^{5}+12\beta q^{7}-21q^{8}+\cdots\)
99.4.d.c	$99$	$4$	99.d	33.d	$2$	$8$	$8$	$5.841$	8.0.\(\cdots\).4	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(5+\beta _{3})q^{4}-5\beta _{6}q^{5}+(-2\beta _{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(99, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(99, [\chi]) \cong \)