Space of modular forms of level 124, weight 4, and Character 124.p

• Label: 124.4.p
• Level: $124$
• Weight: $4$
• Character orbit: 124.p
• Rep. character: $\chi_{124}(3,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $368$
• Newform subspaces: $1$
• Sturm bound: $64$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	124.p (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 124 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(64\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(124, [\chi])\).

	Total	New	Old
Modular forms	400	400	0
Cusp forms	368	368	0
Eisenstein series	32	32	0

Trace form

\( 368 q - 6 q^{2} + 6 q^{4} - 8 q^{5} - 9 q^{6} - 57 q^{8} + 360 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(124, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
124.4.p.a	$124$	$4$	124.p	124.p	$30$	$368$	$46$	$7.316$		None		$4$	$0$	\(-6\)	\(0\)	\(-8\)	\(0\)		$\mathrm{SU}(2)[C_{30}]$