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

• Label: 124.4.e
• Level: $124$
• Weight: $4$
• Character orbit: 124.e
• Rep. character: $\chi_{124}(5,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $16$
• 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.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(64\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	102	16	86
Cusp forms	90	16	74
Eisenstein series	12	0	12

Trace form

\( 16 q - 4 q^{3} - 4 q^{5} - 16 q^{7} - 40 q^{9} + O(q^{10}) \)

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.e.a	$124$	$4$	124.e	31.c	$3$	$2$	$1$	$7.316$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(5\)	\(15\)	\(-29\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(5-5\zeta_{6})q^{3}+15\zeta_{6}q^{5}+(-29+29\zeta_{6})q^{7}+\cdots\)
124.4.e.b	$124$	$4$	124.e	31.c	$3$	$6$	$3$	$7.316$	6.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(-9\)	\(-3\)	\(45\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-3-\beta _{1}-\beta _{2}+3\beta _{3})q^{3}+(2\beta _{1}+\cdots)q^{5}+\cdots\)
124.4.e.c	$124$	$4$	124.e	31.c	$3$	$8$	$4$	$7.316$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-16\)	\(-32\)	$2^{6}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{6}q^{3}+(-\beta _{3}-4\beta _{4}-\beta _{6}+\beta _{7})q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(124, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(124, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(62, [\chi])\)\(^{\oplus 2}\)