Space of modular forms of level 297, weight 1, and Character 297.q

• Label: 297.1.q
• Level: $297$
• Weight: $1$
• Character orbit: 297.q
• Rep. character: $\chi_{297}(43,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	297.q (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 297 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(36\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(297, [\chi])\).

	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

\( 6 q - 3 q^{5} - 3 q^{15} + 6 q^{20} - 3 q^{25} - 3 q^{27} - 3 q^{31} - 3 q^{33} + 6 q^{36} - 3 q^{44} - 3 q^{47} - 3 q^{48} - 3 q^{59} - 3 q^{64} + 6 q^{67} + 6 q^{75} + 3 q^{89} + 6 q^{93} + 6 q^{97}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(297, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
297.1.q.a	$297$	$1$	297.q	297.q	$18$	$6$	$1$	$0.148$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-11}) \)	None		✓	✓	✓	297.1.q.a	$4$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$1$		\(q+\zeta_{18}^{8}q^{3}+\zeta_{18}^{2}q^{4}+(-\zeta_{18}^{3}-\zeta_{18}^{7}+\cdots)q^{5}+\cdots\)