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

• Label: 1764.1.co
• Level: $1764$
• Weight: $1$
• Character orbit: 1764.co
• Rep. character: $\chi_{1764}(73,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $336$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1764.co (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{42})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(336\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	156	12	144
Cusp forms	12	12	0
Eisenstein series	144	0	144

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	12	0	0	0

Trace form

\( 12 q - q^{7} + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1764.1.co.a	$1764$	$1$	1764.co	49.h	$42$	$12$	$1$	$0.880$	\(\Q(\zeta_{21})\)	$D_{42}$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	1764.1.co.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$		\(q-\zeta_{42}^{16}q^{7}+(-\zeta_{42}^{8}+\zeta_{42}^{10})q^{13}+\cdots\)