Space of modular forms of level 399, weight 1, and Character 399.ch

• Label: 399.1.ch
• Level: $399$
• Weight: $1$
• Character orbit: 399.ch
• Rep. character: $\chi_{399}(23,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $53$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 399 = 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	399.ch (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 399 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(53\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(399, [\chi])\).

	Total	New	Old
Modular forms	30	30	0
Cusp forms	6	6	0
Eisenstein series	24	24	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

\( 6 q - 3 q^{12} - 3 q^{13} + 6 q^{19} - 3 q^{21} - 3 q^{27} - 3 q^{43} + 6 q^{52} - 3 q^{61} - 3 q^{64} - 3 q^{67} - 3 q^{73} - 3 q^{75} - 3 q^{79} - 3 q^{91} + 6 q^{93}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(399, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
399.1.ch.a	$399$	$1$	399.ch	399.bh	$18$	$6$	$1$	$0.199$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	399.1.ca.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{18}^{7}q^{3}-\zeta_{18}^{5}q^{4}+\zeta_{18}^{8}q^{7}+\cdots\)