Space of modular forms of level 124, weight 5, and Character 124.c

• Label: 124.5.c
• Level: $124$
• Weight: $5$
• Character orbit: 124.c
• Rep. character: $\chi_{124}(61,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $1$
• Sturm bound: $80$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	124.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(80\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(124, [\chi])\).

	Total	New	Old
Modular forms	67	10	57
Cusp forms	61	10	51
Eisenstein series	6	0	6

Trace form

\( 10 q - 6 q^{5} - 2 q^{7} - 146 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(124, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
124.5.c.a	$124$	$5$	124.c	31.b	$2$	$10$	$10$	$12.818$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(-2\)	$2^{9}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-1+\beta _{3})q^{5}-\beta _{4}q^{7}+(-15+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(124, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(124, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(62, [\chi])\)\(^{\oplus 2}\)