Space of modular forms of level 273, weight 1, and Character 273.s

• Label: 273.1.s
• Level: $273$
• Weight: $1$
• Character orbit: 273.s
• Rep. character: $\chi_{273}(74,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $37$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	273.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 273 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(37\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(273, [\chi])\).

	Total	New	Old
Modular forms	14	14	0
Cusp forms	6	6	0
Eisenstein series	8	8	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	4	0	0

Trace form

\( 6 q - q^{3} + 2 q^{4} - 2 q^{6} - 3 q^{7} + q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(273, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
273.1.s.a	$273$	$1$	273.s	273.s	$6$	$2$	$1$	$0.136$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None		✓			273.1.s.a	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q+\zeta_{6}^{2}q^{3}+q^{4}+\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots\)
273.1.s.b	$273$	$1$	273.s	273.s	$6$	$4$	$2$	$0.136$	\(\Q(\zeta_{12})\)	$A_{4}$	None	None		✓	✓		273.1.s.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-\zeta_{12}^{3}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{5}q^{5}+\cdots\)