Space of modular forms of level 972, weight 1, and Character 972.g

• Label: 972.1.g
• Level: $972$
• Weight: $1$
• Character orbit: 972.g
• Rep. character: $\chi_{972}(161,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $162$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 972 = 2^{2} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	972.g (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(162\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(972, [\chi])\).

	Total	New	Old
Modular forms	68	4	64
Cusp forms	14	4	10
Eisenstein series	54	0	54

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q - q^{7} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(972, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
972.1.g.a	$972$	$1$	972.g	9.d	$6$	$2$	$1$	$0.485$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q+\zeta_{6}^{2}q^{7}+\zeta_{6}q^{13}-q^{19}+\zeta_{6}^{2}q^{25}+\cdots\)
972.1.g.b	$972$	$1$	972.g	9.d	$6$	$2$	$1$	$0.485$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$		\(q-\zeta_{6}^{2}q^{7}-\zeta_{6}q^{13}+q^{19}+\zeta_{6}^{2}q^{25}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(972, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(972, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(243, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(486, [\chi])\)\(^{\oplus 2}\)