Space of modular forms of level 273, weight 2, and trivial character

• Label: 273.2.a
• Level: $273$
• Weight: $2$
• Character orbit: 273.a
• Rep. character: $\chi_{273}(1,\cdot)$
• Character field: $\Q$
• Dimension: $11$
• Newform subspaces: $5$
• Sturm bound: $74$
• Trace bound: $2$

Defining parameters

Level:	$N$	$=$	$273 = 3 \cdot 7 \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	273.a (trivial)
Character field:			$\Q$
Newform subspaces:			$5$
Sturm bound:			$74$
Trace bound:			$2$
Distinguishing $T_p$:			$2$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(273))$.

	Total	New	Old
Modular forms	40	11	29
Cusp forms	33	11	22
Eisenstein series	7	0	7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$3$	$7$	$13$	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
$+$	$+$	$+$	$+$		$4$	$3$	$1$		$4$	$3$	$1$		$0$	$0$	$0$
$+$	$+$	$-$	$-$		$5$	$0$	$5$		$4$	$0$	$4$		$1$	$0$	$1$
$+$	$-$	$+$	$-$		$5$	$2$	$3$		$4$	$2$	$2$		$1$	$0$	$1$
$+$	$-$	$-$	$+$		$4$	$1$	$3$		$3$	$1$	$2$		$1$	$0$	$1$
$-$	$+$	$+$	$-$		$6$	$1$	$5$		$5$	$1$	$4$		$1$	$0$	$1$
$-$	$+$	$-$	$+$		$5$	$0$	$5$		$4$	$0$	$4$		$1$	$0$	$1$
$-$	$-$	$+$	$+$		$5$	$0$	$5$		$4$	$0$	$4$		$1$	$0$	$1$
$-$	$-$	$-$	$-$		$6$	$4$	$2$		$5$	$4$	$1$		$1$	$0$	$1$
Plus space			$+$		$18$	$4$	$14$		$15$	$4$	$11$		$3$	$0$	$3$
Minus space			$-$		$22$	$7$	$15$		$18$	$7$	$11$		$4$	$0$	$4$

Trace form

11 * q + q^2 - q^3 + 17 * q^4 - 6 * q^5 + 5 * q^6 + 3 * q^7 - 3 * q^8 + 11 * q^9 - 2 * q^10 - 4 * q^11 + q^12 - q^13 + q^14 + 2 * q^15 + 25 * q^16 - 10 * q^17 + q^18 + 4 * q^19 - 42 * q^20 + 3 * q^21 - 12 * q^22 - 4 * q^23 + 9 * q^24 - 7 * q^25 - 3 * q^26 - q^27 + 5 * q^28 - 2 * q^29 - 2 * q^30 - 8 * q^31 - 35 * q^32 - 4 * q^33 - 38 * q^34 - 2 * q^35 + 17 * q^36 + 10 * q^37 + 12 * q^38 + 7 * q^39 + 14 * q^40 - 18 * q^41 - 3 * q^42 + 20 * q^44 - 6 * q^45 + 16 * q^46 - 15 * q^48 + 11 * q^49 + 23 * q^50 + 6 * q^51 + q^52 - 10 * q^53 + 5 * q^54 - 8 * q^55 + 21 * q^56 + 12 * q^57 - 2 * q^58 - 36 * q^59 - 18 * q^60 + 18 * q^61 - 8 * q^62 + 3 * q^63 + 33 * q^64 - 2 * q^65 - 12 * q^66 - 4 * q^67 - 14 * q^68 + 16 * q^69 - 2 * q^70 + 24 * q^71 - 3 * q^72 - 2 * q^73 - 26 * q^74 + 17 * q^75 - 60 * q^76 + 4 * q^77 + q^78 - 4 * q^79 - 50 * q^80 + 11 * q^81 + 42 * q^82 - 4 * q^83 + 5 * q^84 + 28 * q^85 + 44 * q^86 - 6 * q^87 - 108 * q^88 - 26 * q^89 - 2 * q^90 + 7 * q^91 + 8 * q^92 + 32 * q^93 + 48 * q^94 - 4 * q^95 + 33 * q^96 - 26 * q^97 + q^98 - 4 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(273))$ 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					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	7	13
273.2.a.a	$273$	$2$	273.a	1.a	$1$	$1$	$1$	$2.180$	$\Q$	None	✓	✓	✓	✓	273.2.a.a	$1$	$1$	$-2$	$-1$	$-1$	$1$		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}+q^{7}+\cdots$
273.2.a.b	$273$	$2$	273.a	1.a	$1$	$1$	$1$	$2.180$	$\Q$	None	✓	✓	✓	✓	273.2.a.b	$1$	$0$	$2$	$1$	$1$	$-1$		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}-q^{7}+\cdots$
273.2.a.c	$273$	$2$	273.a	1.a	$1$	$2$	$2$	$2.180$	$\Q(\sqrt{2})$	None	✓	✓	✓	✓	273.2.a.c	$1$	$0$	$2$	$-2$	$0$	$2$		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots$
273.2.a.d	$273$	$2$	273.a	1.a	$1$	$3$	$3$	$2.180$	3.3.316.1	None	✓	✓	✓	✓	273.2.a.d	$1$	$1$	$-2$	$-3$	$-3$	$-3$		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}-q^{3}+(2-2\beta _{1}+\beta _{2})q^{4}+\cdots$
273.2.a.e	$273$	$2$	273.a	1.a	$1$	$4$	$4$	$2.180$	4.4.17428.1	None	✓	✓	✓	✓	273.2.a.e	$1$	$0$	$1$	$4$	$-3$	$4$		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(273))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_0(273)) \simeq$ $S_{2}^{\mathrm{new}}(\Gamma_0(21))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(39))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_0(91))$$^{\oplus 2}$