Space of modular forms of level 1764, weight 1, and Character 1764.q

• Label: 1764.1.q
• Level: $1764$
• Weight: $1$
• Character orbit: 1764.q
• Rep. character: $\chi_{1764}(215,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $336$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1764.q (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 84 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(336\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1764, [\chi])\).

	Total	New	Old
Modular forms	88	24	64
Cusp forms	24	24	0
Eisenstein series	64	0	64

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	24	0	0	0

Trace form

\( 24 q + 8 q^{4} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1764, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1764.1.q.a	$1764$	$1$	1764.q	84.j	$6$	$8$	$4$	$0.880$	\(\Q(\zeta_{24})\)	$D_{4}$	\(\Q(\sqrt{-7}) \)	None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{9}q^{8}+\cdots\)
1764.1.q.b	$1764$	$1$	1764.q	84.j	$6$	$16$	$8$	$0.880$	\(\Q(\zeta_{48})\)	$D_{8}$	\(\Q(\sqrt{-1}) \)	None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$		\(q-\zeta_{48}^{20}q^{2}-\zeta_{48}^{16}q^{4}+(-\zeta_{48}^{5}+\cdots)q^{5}+\cdots\)