Space of modular forms of level 72, weight 2, and Character 72.i

• Label: 72.2.i
• Level: $72$
• Weight: $2$
• Character orbit: 72.i
• Rep. character: $\chi_{72}(25,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(24\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(72, [\chi])\).

	Total	New	Old
Modular forms	32	6	26
Cusp forms	16	6	10
Eisenstein series	16	0	16

Trace form

\( 6 q + q^{3} + 2 q^{5} - q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(72, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
72.2.i.a	$72$	$2$	72.i	9.c	$3$	$2$	$1$	$0.575$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(1\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+3\zeta_{6}q^{7}+\cdots\)
72.2.i.b	$72$	$2$	72.i	9.c	$3$	$4$	$2$	$0.575$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(1\)	\(1\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2}-2\beta _{3})q^{5}+(1-2\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(72, [\chi])\) into lower level spaces

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