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	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)	\(2\)
\(+\)	\(-\)	\(-\)	\(+\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)	\(4\)
Plus space			\(+\)	\(4\)
Minus space			\(-\)	\(7\)

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

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