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

• Label: 124.3.c
• Level: $124$
• Weight: $3$
• Character orbit: 124.c
• Rep. character: $\chi_{124}(61,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $1$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	35	6	29
Cusp forms	29	6	23
Eisenstein series	6	0	6

Trace form

\( 6 q + 6 q^{5} - 14 q^{7} - 14 q^{9} + O(q^{10}) \)

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.c.a	$124$	$3$	124.c	31.b	$2$	$2$	$2$	$3.379$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-12\)	\(-20\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{3}-6q^{5}-10q^{7}-3q^{9}+5\zeta_{6}q^{11}+\cdots\)
124.3.c.b	$124$	$3$	124.c	31.b	$2$	$4$	$4$	$3.379$	4.0.63368.1	None		$2$	$0$	\(0\)	\(0\)	\(18\)	\(6\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(4+\beta _{3})q^{5}+(2-\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(124, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(124, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(62, [\chi])\)\(^{\oplus 2}\)