Space of modular forms of level 72, weight 4, and Character 72.f

• Label: 72.4.f
• Level: $72$
• Weight: $4$
• Character orbit: 72.f
• Rep. character: $\chi_{72}(35,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	72.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(48\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(72, [\chi])\).

	Total	New	Old
Modular forms	40	12	28
Cusp forms	32	12	20
Eisenstein series	8	0	8

Trace form

\( 12 q - 12 q^{4} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(72, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
72.4.f.a	$72$	$4$	72.f	24.f	$2$	$12$	$12$	$4.248$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{15}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+(-1+\beta _{6})q^{4}-\beta _{5}q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(72, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(72, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)