Space of modular forms of level 72, weight 3, and Character 72.e

• Label: 72.3.e
• Level: $72$
• Weight: $3$
• Character orbit: 72.e
• Rep. character: $\chi_{72}(17,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	72.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(36\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(72, [\chi])\).

	Total	New	Old
Modular forms	32	2	30
Cusp forms	16	2	14
Eisenstein series	16	0	16

Trace form

\( 2 q + 24 q^{7} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(72, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
72.3.e.a	$72$	$3$	72.e	3.b	$2$	$2$	$2$	$1.962$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(24\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+5\beta q^{5}+12q^{7}-4\beta q^{11}-8q^{13}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(72, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(72, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)