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

• Label: 124.4.d
• Level: $124$
• Weight: $4$
• Character orbit: 124.d
• Rep. character: $\chi_{124}(123,\cdot)$
• Character field: $\Q$
• Dimension: $46$
• Newform subspaces: $3$
• Sturm bound: $64$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	124.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 124 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(64\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

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

	Total	New	Old
Modular forms	50	50	0
Cusp forms	46	46	0
Eisenstein series	4	4	0

Trace form

\( 46 q - 2 q^{2} + 10 q^{4} - 4 q^{5} + 25 q^{8} + 374 q^{9} + O(q^{10}) \)

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.d.a	$124$	$4$	124.d	124.d	$2$	$2$	$2$	$7.316$	\(\Q(\sqrt{-31}) \)	\(\Q(\sqrt{-31}) \)		$4$	$0$	\(1\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{2}+(-8+\beta )q^{4}-2q^{5}+(6-12\beta )q^{7}+\cdots\)
124.4.d.b	$124$	$4$	124.d	124.d	$2$	$4$	$4$	$7.316$	\(\Q(\sqrt{-3}, \sqrt{-31})\)	\(\Q(\sqrt{-31}) \)		$4$	$0$	\(-1\)	\(0\)	\(4\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+(-1-\beta _{1}-\beta _{3})q^{2}+(4+\beta _{1}+2\beta _{2}+\cdots)q^{4}+\cdots\)
124.4.d.c	$124$	$4$	124.d	124.d	$2$	$40$	$40$	$7.316$		None		$4$	$0$	\(-2\)	\(0\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$