Space of modular forms of level 407, weight 1, and Character 407.t

• Label: 407.1.t
• Level: $407$
• Weight: $1$
• Character orbit: 407.t
• Rep. character: $\chi_{407}(120,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $38$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 407 = 11 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	407.t (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 407 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(38\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(407, [\chi])\).

	Total	New	Old
Modular forms	18	18	0
Cusp forms	6	6	0
Eisenstein series	12	12	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	0	0

Trace form

\( 6 q - 3 q^{3} - 3 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(407, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
407.1.t.a	$407$	$1$	407.t	407.t	$18$	$6$	$1$	$0.203$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-11}) \)	None		✓	✓	✓	407.1.t.a	$4$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{18}^{2}+\zeta_{18}^{6})q^{3}-\zeta_{18}q^{4}+\zeta_{18}^{7}q^{5}+\cdots\)