Space of modular forms of level 72, weight 7, and Character 72.p

• Label: 72.7.p
• Level: $72$
• Weight: $7$
• Character orbit: 72.p
• Rep. character: $\chi_{72}(43,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $140$
• Newform subspaces: $2$
• Sturm bound: $84$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	72.p (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 72 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(84\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(72, [\chi])\).

	Total	New	Old
Modular forms	148	148	0
Cusp forms	140	140	0
Eisenstein series	8	8	0

Trace form

\( 140 q - q^{2} - 4 q^{3} - q^{4} - 193 q^{6} - 274 q^{8} - 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(72, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
72.7.p.a	$72$	$7$	72.p	72.p	$6$	$4$	$2$	$16.564$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(16\)	\(-46\)	\(0\)	\(0\)	$2^{2}\cdot 5^{2}$	$\mathrm{U}(1)[D_{6}]$	\(q+8\beta _{2}q^{2}+(-\beta _{1}-23\beta _{2}+\beta _{3})q^{3}+\cdots\)
72.7.p.b	$72$	$7$	72.p	72.p	$6$	$136$	$68$	$16.564$		None		$4$	$0$	\(-17\)	\(42\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$