Space of modular forms of level 1407, weight 1, and Character 1407.ct

• Label: 1407.1.ct
• Level: $1407$
• Weight: $1$
• Character orbit: 1407.ct
• Rep. character: $\chi_{1407}(80,\cdot)$
• Character field: $\Q(\zeta_{66})$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $181$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1407 = 3 \cdot 7 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1407.ct (of order \(66\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1407 \)
Character field:			\(\Q(\zeta_{66})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(181\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1407, [\chi])\).

	Total	New	Old
Modular forms	100	100	0
Cusp forms	20	20	0
Eisenstein series	80	80	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	20	0	0	0

Trace form

\( 20 q - q^{3} - q^{4} - 2 q^{7} + q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1407, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1407.1.ct.a	$1407$	$1$	1407.ct	1407.bt	$66$	$20$	$1$	$0.702$	\(\Q(\zeta_{33})\)	$D_{66}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(-2\)	$1$		\(q-\zeta_{66}^{10}q^{3}+\zeta_{66}^{29}q^{4}+\zeta_{66}^{24}q^{7}+\cdots\)