Space of modular forms of level 273, weight 2, and Character 273.bw

• Label: 273.2.bw
• Level: $273$
• Weight: $2$
• Character orbit: 273.bw
• Rep. character: $\chi_{273}(11,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $132$
• Newform subspaces: $2$
• Sturm bound: $74$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bw (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 273 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(74\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(273, [\chi])\).

	Total	New	Old
Modular forms	164	164	0
Cusp forms	132	132	0
Eisenstein series	32	32	0

Trace form

\( 132 q - 4 q^{3} - 12 q^{4} - 4 q^{6} - 16 q^{7} - 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(273, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
273.2.bw.a	$273$	$2$	273.bw	273.aw	$12$	$4$	$1$	$2.180$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(-2\zeta_{12}+\zeta_{12}^{3})q^{3}+(-2\zeta_{12}+2\zeta_{12}^{3})q^{4}+\cdots\)
273.2.bw.b	$273$	$2$	273.bw	273.aw	$12$	$128$	$32$	$2.180$		None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(-16\)		$\mathrm{SU}(2)[C_{12}]$