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

• Label: 297.1.h
• Level: $297$
• Weight: $1$
• Character orbit: 297.h
• Rep. character: $\chi_{297}(10,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $2$
• 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.h (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 99 \)
Character field:			\(\Q(\zeta_{6})\)
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	6	12
Cusp forms	6	2	4
Eisenstein series	12	4	8

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q - q^{4} - q^{5} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
297.1.h.a	$297$	$1$	297.h	99.h	$6$	$2$	$1$	$0.148$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-11}) \)	None		$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{11}-\zeta_{6}q^{16}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(297, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(297, [\chi]) \cong \)