Space of modular forms of level 124, weight 2, and Character 124.j

• Label: 124.2.j
• Level: $124$
• Weight: $2$
• Character orbit: 124.j
• Rep. character: $\chi_{124}(15,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $56$
• Newform subspaces: $2$
• Sturm bound: $32$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	124.j (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 124 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(32\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(124, [\chi])\).

	Total	New	Old
Modular forms	72	72	0
Cusp forms	56	56	0
Eisenstein series	16	16	0

Trace form

\( 56 q - 3 q^{2} + q^{4} - 16 q^{5} + 9 q^{8} - 16 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(124, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
124.2.j.a	$124$	$2$	124.j	124.j	$10$	$8$	$2$	$0.990$	\(\Q(\zeta_{20})\)	None		$4$	$0$	\(-2\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(-1+\zeta_{20}^{2}-\zeta_{20}^{3}-\zeta_{20}^{4}+\zeta_{20}^{6}+\cdots)q^{2}+\cdots\)
124.2.j.b	$124$	$2$	124.j	124.j	$10$	$48$	$12$	$0.990$		None		$4$	$0$	\(-1\)	\(0\)	\(-12\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$