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

• Label: 124.2.d
• Level: $124$
• Weight: $2$
• Character orbit: 124.d
• Rep. character: $\chi_{124}(123,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $3$
• Sturm bound: $32$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(32\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

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

	Total	New	Old
Modular forms	18	18	0
Cusp forms	14	14	0
Eisenstein series	4	4	0

Trace form

\( 14 q - 2 q^{2} - 6 q^{4} - 4 q^{5} + q^{8} + 6 q^{9} + O(q^{10}) \)

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.d.a	$124$	$2$	124.d	124.d	$2$	$4$	$4$	$0.990$	\(\Q(i, \sqrt{6})\)	None		$4$	$0$	\(-4\)	\(0\)	\(4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}-2\beta _{1}q^{4}+\cdots\)
124.2.d.b	$124$	$2$	124.d	124.d	$2$	$4$	$4$	$0.990$	\(\Q(\sqrt{6}, \sqrt{-7})\)	None		$4$	$0$	\(2\)	\(0\)	\(-8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(-2-\beta _{1})q^{4}-2q^{5}+\cdots\)
124.2.d.c	$124$	$2$	124.d	124.d	$2$	$6$	$6$	$0.990$	6.0.21717639.1	\(\Q(\sqrt{-31}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{5}q^{2}-\beta _{3}q^{4}+(\beta _{3}+\beta _{4}-\beta _{5})q^{5}+\cdots\)