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

• Label: 1764.1.y
• Level: $1764$
• Weight: $1$
• Character orbit: 1764.y
• Rep. character: $\chi_{1764}(667,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $14$
• Newform subspaces: $4$
• Sturm bound: $336$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1764.y (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(336\)
Trace bound:			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	84	22	62
Cusp forms	20	14	6
Eisenstein series	64	8	56

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	14	0	0	0

Trace form

\( 14 q - q^{2} - 3 q^{4} + 2 q^{8} + O(q^{10}) \)

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.y.a	$1764$	$1$	1764.y	28.g	$6$	$2$	$1$	$0.880$	\(\Q(\sqrt{-3}) \)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \)	\(\Q(\sqrt{7}) \)		$8$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+q^{8}-\zeta_{6}q^{16}+\cdots\)
1764.1.y.b	$1764$	$1$	1764.y	28.g	$6$	$4$	$2$	$0.880$	\(\Q(\sqrt{2}, \sqrt{-3})\)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None		$8$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
1764.1.y.c	$1764$	$1$	1764.y	28.g	$6$	$4$	$2$	$0.880$	\(\Q(\zeta_{12})\)	$D_{2}$	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-21}) \)	\(\Q(\sqrt{3}) \)		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{8}+\zeta_{12}^{5}q^{11}+\cdots\)
1764.1.y.d	$1764$	$1$	1764.y	28.g	$6$	$4$	$2$	$0.880$	\(\Q(\sqrt{2}, \sqrt{-3})\)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None		$8$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1764, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1764, [\chi]) \cong \)