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

• Label: 72.4.i
• Level: $72$
• Weight: $4$
• Character orbit: 72.i
• Rep. character: $\chi_{72}(25,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $18$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	72.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(48\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	80	18	62
Cusp forms	64	18	46
Eisenstein series	16	0	16

Trace form

\( 18 q + q^{3} - 10 q^{5} + 29 q^{9} + O(q^{10}) \)

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.i.a	$72$	$4$	72.i	9.c	$3$	$8$	$4$	$4.248$	8.0.5206055409.1	None		$2$	$0$	\(0\)	\(-3\)	\(-5\)	\(3\)	$2^{6}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{5}q^{3}+(2\beta _{1}-\beta _{2}+\beta _{4})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
72.4.i.b	$72$	$4$	72.i	9.c	$3$	$10$	$5$	$4.248$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(4\)	\(-5\)	\(-3\)	$2^{8}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{4}q^{3}+(-1+\beta _{1}+\beta _{8})q^{5}+(\beta _{4}+\cdots)q^{7}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(72, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)