Space of modular forms of level 273, weight 3, and Character 273.w

• Label: 273.3.w
• Level: $273$
• Weight: $3$
• Character orbit: 273.w
• Rep. character: $\chi_{273}(116,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $140$
• Newform subspaces: $4$
• Sturm bound: $112$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	273.w (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 273 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(112\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(273, [\chi])\).

	Total	New	Old
Modular forms	156	156	0
Cusp forms	140	140	0
Eisenstein series	16	16	0

Trace form

\( 140 q - 2 q^{3} - 132 q^{4} - 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(273, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
273.3.w.a	$273$	$3$	273.w	273.w	$6$	$2$	$1$	$7.439$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(-3\)	\(0\)	\(-13\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q-3\zeta_{6}q^{3}+4\zeta_{6}q^{4}+(-5-3\zeta_{6})q^{7}+\cdots\)
273.3.w.b	$273$	$3$	273.w	273.w	$6$	$2$	$1$	$7.439$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(-3\)	\(0\)	\(13\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q-3\zeta_{6}q^{3}+4\zeta_{6}q^{4}+(5+3\zeta_{6})q^{7}+\cdots\)
273.3.w.c	$273$	$3$	273.w	273.w	$6$	$16$	$8$	$7.439$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}-\beta _{10})q^{2}+(\beta _{4}-\beta _{9})q^{3}+(\beta _{4}+\cdots)q^{4}+\cdots\)
273.3.w.d	$273$	$3$	273.w	273.w	$6$	$120$	$60$	$7.439$		None		$8$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$