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

• Label: 273.2.r
• Level: $273$
• Weight: $2$
• Character orbit: 273.r
• Rep. character: $\chi_{273}(68,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $66$
• 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.r (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$273$
Character field:			$\Q(\zeta_{6})$
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	82	82	0
Cusp forms	66	66	0
Eisenstein series	16	16	0

Trace form

66 * q - 3 * q^3 - 60 * q^4 + 12 * q^6 - 6 * q^7 - q^9 - 6 * q^10 + 10 * q^13 - 9 * q^15 + 40 * q^16 + 2 * q^18 - 21 * q^19 + 7 * q^21 + 10 * q^22 - 18 * q^24 - 19 * q^25 - 6 * q^28 + 8 * q^30 - 39 * q^31 - 45 * q^33 + 6 * q^36 - 22 * q^37 + 30 * q^39 + 90 * q^40 + 3 * q^42 - 12 * q^43 - 18 * q^48 - 4 * q^49 - 10 * q^51 - 52 * q^52 - 18 * q^55 - 26 * q^57 + 30 * q^58 + 55 * q^60 - 45 * q^61 + 28 * q^63 - 68 * q^64 + 75 * q^66 + 33 * q^67 + 33 * q^69 + 20 * q^70 + 17 * q^72 + 60 * q^73 + 12 * q^76 - 71 * q^78 + 33 * q^79 + 7 * q^81 - 18 * q^82 - 141 * q^84 - 2 * q^85 - 46 * q^88 - 2 * q^91 - 26 * q^93 + 36 * q^94 + 30 * q^96 - 33 * q^97 + 22 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
273.2.r.a	$273$	$2$	273.r	273.r	$6$	$2$	$1$	$2.180$	$\Q(\sqrt{-3})$	$\Q(\sqrt{-3})$		✓			273.2.r.a	$4$	$0$	$0$	$-3$	$0$	$4$	$1$	$\mathrm{U}(1)[D_{6}]$	$q+(-1-\zeta_{6})q^{3}+2q^{4}+(1+2\zeta_{6})q^{7}+\cdots$
273.2.r.b	$273$	$2$	273.r	273.r	$6$	$64$	$32$	$2.180$		None		✓	✓		273.2.r.b	$4$	$0$	$0$	$0$	$0$	$-10$		$\mathrm{SU}(2)[C_{6}]$