Space of modular forms of level 124, weight 3, and Character 124.l

• Label: 124.3.l
• Level: $124$
• Weight: $3$
• Character orbit: 124.l
• Rep. character: $\chi_{124}(35,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $120$
• Newform subspaces: $1$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	124.l (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 124 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(48\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(124, [\chi])\).

	Total	New	Old
Modular forms	136	136	0
Cusp forms	120	120	0
Eisenstein series	16	16	0

Trace form

\( 120 q - 3 q^{2} + q^{4} - 16 q^{5} - 10 q^{6} + 27 q^{8} + 72 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(124, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
124.3.l.a	$124$	$3$	124.l	124.l	$10$	$120$	$30$	$3.379$		None		$4$	$0$	\(-3\)	\(0\)	\(-16\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$